Login

Contact Us
Calculus and Above
Calculus Questions? Ask a Mathematician for Answers ASAP
Not a Calculus and Above Question?
How JustAnswer Works:
Ask an Expert
Experts are full of valuable knowledge and are ready to help with any question. Credentials confirmed by a Fortune 500 verification firm.
Get a Professional Answer
Via email, text message, or notification as you wait on our site.
Ask follow up questions if you need to.
100% Satisfaction Guarantee
Rate the answer you receive.
Ask Calc101 Your Own Question
Calc101
,
Master's Degree
Category:
Calculus and Above
Satisfied Customers:
0
Experience:
Help from a real teacher for questions in PreCalculus and Calculus.
64828298
Type Your Calculus and Above Question Here...
Calc101 is online now
This question uses the function f(x) = 2x^3  9x^2 + 24x +
Customer Question
This question uses the function f(x) = 2x^3  9x^2 + 24x + 40
Find the stationary points of this function
B. Using the strategy to apply the first derivative test, classify the left hand stationary point found in the first question
Then using second derivative test classify the right hand stationary point found in first question
C. Find the y coordinate of each of the stationary points on the graph of the function f(x), and evaluate f(0)
D. Draw a graph of the function f(x)
2a. Simplify the answers where appropriate
Write down the derivative of each of the functions:
F(x) = x^4 and g(x) = sin(5x)
Hence by using product rule, differentiate the function
K(x) = x^4sin(5x)
Write down the derivative of each of the functions f(t) = e^6t and g(t) = t^3 + 8
Hence by using quotient rule, differentiate the function
K(t) = e^6t/t^3 + 8 (t > 2)
Write down derivative of the function f(x) = 6cos(1/3x)
Hence using the composite rule differentiate the function k(x) = ln (6cos(1/3x)) (3/2 delta < x 0)
h(u) = cos^2 (6u)
B. Evaluate indefinite integral with 8 at top and 6 at bottom x(4 + 7x^2)dx
C. Write down a definite integral that will give the value of the area under the curve y=x^2sin(3/4x) between x = 1/3 delta and x = delta
( do not evaluate the integral by hand)
Use mathcad to find the area described in previous question giving answer to 4 decimal places and give print out of the working
4. A rocket is modelled by a particle that moves along a vertical line. From launch the rocket rises until it's motor cuts out after 17 seconds. At this time it has reached a height of 580 metres above launch pad and attained an upward velocity of 120ms1. from this time on the rocket has a constant upward acceleration of 10ms2 ( due to gravity effect)
Choose the s axis ( for position of particle that represents the rocket) to point upwards with origin at launch pad. Take t = 0 to be the time when rocket motor cuts
What is the max height above launch pad reached by rocket?
How long from launch does rocket take to reach this max height?
After how long from launch does rocket crash onto launch pad?
Give your answers in seconds to 1 decimal place
5. Solve the initial value problem dy/dx = sin(4x)/3+cos(4x). Y = 5 when x = 0
Show where c is an arbitrary constant in this equation
Indefinate integral 2e^2x  5/(e^2x  5x)^2/3 dx=3(e^2x  5x)^1/3 + c
Hence find it's implicit form, the general solution of the differential equation
Dy/dx = 2y^1/2(2e^2x 5)/3(e^2x 5x)^2/3 (y>0)
Find corresponding particular solution (in implicit form) that satisfies the initial condition y=1 when x = 0
Find the explicit form of this particular solution
What is the value of y given by this particular solution when x =2? Give your answer to 4 sig figs
Submitted:
2 years ago.
Category:
Calculus and Above
Share this conversation
Expert:
AngelaMod
replied 2 years ago.
Hi, I’m a moderator for this topic and I wonder whether you’re still waiting for an answer. If you are, please let me know and I will do my best to find an Expert to assist you right away. If not, feel free to let me know and I will cancel this question for you. Thank you!
Ask Your Own Calculus and Above Question
Customer:
replied 2 years ago.
Hello yes I'm still waiting for an expert to answer. Thank you very much for getting back and helping
Expert:
AngelaMod
replied 2 years ago.
Sometimes, finding the right Expert can take a little longer than expected and we thank you greatly for your understanding. We’ll be in touch again shortly.
Ask Your Own Calculus and Above Question
Expert:
Calc101
replied 2 years ago.
Ok, I can definitely help you with the first part.
So, a stationary point is the same as a critical point (if you know that term better). Basically we need to find where the derivative is equal to 0. So, let's differentiate f(x).
f'(x)=6x^218x+24
Now, set the derivative equal to 0, and you can solve for what the stationary points are.
0=6x^218x+24
0=x^2+3x4
0=(x+4)(x1)
Therefore, x=4 and x=1 are your stationary points.
B. To use the first derivative test, we will test what the derivative does to the left of x=4 and to the right of x=4.
To the left of x=4, f'(x)0.
When the slope goes from negative to positive, we have a relative minimum.
For the second derivative test, we must of course first find the the second derivative.
f''(x)=12x18
Now, we test f''(1). If it is less than 0, we have a maximum, and if it is greater than 0, we have a minimum.
f''(1)=6
Therefore, we have a relative maximum.
We can also verify this using the first derivative test, since to the left of x=1 (and to the right of x=4), f'(x)>0 and to the right of x=1, f'(x)<0, which means we have a relative maximum.
C. f(0)=53
f(4)=72
f(1)=40
2.
A. f'(x)=4x^3
g'(x)=5cos(5x) (this involves the chain rule where we must take the derivative of the outer function (sin) and then multiply it by the derivative of the inside function (5x) which is 5).
The derivative using the product rule is fg'+gf'.
So, we take x^4(5cos(5x))+sin(5x)(4x^3)
Now for the second one:
f'(t)=6e^6t, since we take the derivative of e^t which is just e^t and multiply it by the derivative of 6t (which is 6). This is basically u substitution where u=6t and du=6.
g'(t)= 3t^2
The quotient rule is (gf'fg')/g^2 PLEASE NOTE: In the quotient rule the top (gf'fg') matters in terms of order. The product rule does not. It can be written as fg'+gf' or gf'+fg'.
So, we take ((t^3+8)(6e^6t)(e^6t)(3t^2))/(t^3+8)^2
Now to the next part,
f(x)=6cos(1/3x)
This utilizes the chain rule again.
We take the derivative of the outside, 6cos, which is 6sin (please don't forget that cosine has the negative when you take the derivative, whereas the derivative of sine does not). Then take the derivative of the inside ((1/3)x) which is 1/3.
We get, 6sin((1/3)x)*1/3, which is 2sin((1/3)x).
So, using the composite rule (AKA chain rule), we basically take the derivative of the outside, ln(u) (where u is the inside function), which is 1/u du.
du is the derivative of the inside, namely, 2sin((1/3)x).
So, the answer is 1/(6cos(1/3x))*(2sin((1/3)x)).
B. (First of all, the instructions must be wrong here, since an indefinite integral has no bounds. Definite integration involves the bounds from 6 to 8).
So, this involves u substitution. Make u the function that will result in giving you what is leftover with the dx.
So, let's try u=4+7x^2 since that will leave us with something times xdx. du is the derivative of u. So, du=14x, which means du/14=xdx.
So, we now have (1/14)int(u du,6,8). We put the constant that goes with du in front of the integral when we integrate. The integral of u, is u^2/2, which when we replace is (4+7x^2)/2 from 6 to 8.
Start with the upper bound (8), that gives us, 226. Now plug in the lower bound (6), which gives us 128. Now subtract the lower bound's value from the upper bound's value. 226128=98.
Therefore the answer is 98.
That's what I can help you with at this point. I really hope this is helpful, and if anything doesn't make sense, please feel free to ask me. I hope another expert can help you with the rest of the problems on here. I'll look some things up though, and see if I can come up with some things for your other problems.
Ask Your Own Calculus and Above Question
Customer:
replied 2 years ago.
Thank you very much with your help on this it is very difficult hopefully more experts can help with the remaining questions.
Customer:
replied 2 years ago.
Relist: Incomplete answer.
Share this conversation
JustAnswer in the News:
Askadoc Web sites: If you've got a quick question, you can try to get an answer from sites that say they have various specialists on hand to give quick answers... Justanswer.com.
JustAnswer.com...has seen a spike since October in legal questions from readers about layoffs, unemployment and severance.
Web sites like justanswer.com/legal
...leave nothing to chance.
Traffic on JustAnswer rose 14 percent...and had nearly 400,000 page views in 30 days...inquiries related to stress, high blood pressure, drinking and heart pain jumped 33 percent.
Tory Johnson, GMA Workplace Contributor, discusses workfromhome jobs, such as JustAnswer in which verified Experts answer people’s questions.
I will tell you that...the things you have to go through to be an Expert are quite rigorous.
What Customers are Saying:
Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help.
Mary C.
Freshfield, Liverpool, UK
<
Last

Next
>
Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help.
Mary C.
Freshfield, Liverpool, UK
This expert is wonderful. They truly know what they are talking about, and they actually care about you. They really helped put my nerves at ease. Thank you so much!!!!
Alex
Los Angeles, CA
Thank you for all your help. It is nice to know that this service is here for people like myself, who need answers fast and are not sure who to consult.
GP
Hesperia, CA
I couldn't be more satisfied! This is the site I will always come to when I need a second opinion.
Justin
Kernersville, NC
Just let me say that this encounter has been entirely professional and most helpful. I liked that I could ask additional questions and get answered in a very short turn around.
Esther
Woodstock, NY
Thank you so much for taking your time and knowledge to support my concerns. Not only did you answer my questions, you even took it a step further with replying with more pertinent information I needed to know.
Robin
Elkton, Maryland
He answered my question promptly and gave me accurate, detailed information. If all of your experts are half as good, you have a great thing going here.
Diane
Dallas, TX
Meet The Experts:
SusanAthena
Master's Degree
Satisfied Customers:
98
Tutor for Algebra, Geometry, Statistics. Explaining math in plain English.
<
Last

Next
>
http://ww2.justanswer.com/uploads/homeworklady/20081124_125231_susannewavatar.jpg
SusanAthena's Avatar
SusanAthena
Master's Degree
Satisfied Customers:
98
Tutor for Algebra, Geometry, Statistics. Explaining math in plain English.
http://ww2.justanswer.com/uploads/ED/educatortech/201267_1256_williams4.64x64.jpg
Mr. Gregory White's Avatar
Mr. Gregory White
Master's Degree
Satisfied Customers:
93
M.A., M.S. Education / Educational Administration
http://ww2.justanswer.com/uploads/CO/CosumelEyes/201254_4923_Profile.64x64.jpg
Ray Atkinson's Avatar
Ray Atkinson
Bachelor's Degree
Satisfied Customers:
45
Degrees in Math, Education and Accounting, years and years of tutoring.
http://ww2.justanswer.com/uploads/SO/sonofGauss/201266_20151_PortraitLHW.64x64.jpg
JACUSTOMERyrynbdjl's Avatar
JACUSTOMERyrynbdjl
Master's Degree
Satisfied Customers:
42
I have a MS in Mathematics and I have taught Mathematics for 10 years at the college level.
http://ww2.justanswer.com/uploads/dhouse1940/20100902_133023_DSCN2406.jpg
dhouse1940's Avatar
dhouse1940
Master's Degree
Satisfied Customers:
33
BS mathematics, MS biostatistics, 35+ yrs designing & analyzing biological experiments.
http://ww2.justanswer.com/uploads/AR/arubin9/201224_42617_ArthurRubinedit.64x64.jpg
Dr Arthur Rubin's Avatar
Dr Arthur Rubin
Doctoral Degree
Satisfied Customers:
32
Ph.D. in Mathematics, 1978, from the California Institute of Technology, over 20 published papers
http://ww2.justanswer.com/uploads/DO/Donbacongamer/201236_2337_mathmaster.64x64.jpg
Don's Avatar
Don
Master's Degree
Satisfied Customers:
29
M.S. Astronautical Engineering. Math/Sci/Comp Tutor
Related Calculus and Above Questions
Question
Date Submitted
A. Use the comparison test to determine the convergence or
10/17/2014
10/17/2014
Ryan
I have the same questions as the student did previously. Plus
10/15/2014
10/16/2014
StatisticsExpert
A random sample of 5 accidents resulted in the following number
10/11/2014
10/11/2014
Ryan
How many social robots would need to be sampled in order to
10/11/2014
10/11/2014
Ryan
American and Japanese workers can each produce 4 cars a year.
10/11/2014
10/14/2014
manas11
Recently, the bowling scores of a certain bowler were normally
10/7/2014
10/7/2014
Ryan
Hello. I have to present a stat problem tomorrow. Can you please
10/7/2014
10/7/2014
Ashok Kumar
Create your table in Word as shown on page 578 (which I will
10/6/2014
10/7/2014
StatisticsExpert
Using case Exhiibit 21.11 on page 527 in the textbook,
10/6/2014
10/6/2014
StatisticsExpert
For Ryan..... An important application of regression analysis
9/29/2014
9/29/2014
Ryan
X
Ask a Tutor
Get a Professional Answer. 100% Satisfaction Guaranteed.
81 Tutors are Online Now
Type Your Calculus and Above Question Here...
characters left: