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Ryan
Ryan, Engineer
Category: Calculus and Above
Satisfied Customers: 8883
Experience:  B.S. in Civil Engineering
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Discuss how you would use derivatives to help predict the various

Customer Question

Discuss how you would use derivatives to help predict the various life cycle stages of this curve from development all the way through decline
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Customer: Discuss how you would use derivatives to help predict the various life cycle stages of this curve from development all the way through decline
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Submitted: 7 months ago.
Category: Calculus and Above
Expert:  Mr. Glenn replied 7 months ago.
HiWhen do you need the answer? (how many days from now?)
Customer: replied 7 months ago.
2 hours if possible....I'm trying to answer a discussion question so any tiny bit of help will be appreciated.
Expert:  Mr. Glenn replied 7 months ago.
Also you mentioned there is a curve, can you show or upload that curve?
Customer: replied 7 months ago.
attached
Expert:  Mr. Glenn replied 7 months ago.
Can you kindly accept the small offer below?
Customer: replied 7 months ago.
no thank you....can you answer as best you can here so I can continue. I do not wish to purchase any other services.
Expert:  Ryan replied 7 months ago.
Hi, Thank you for using the site. Do you still need help with this? Ryan
Customer: replied 7 months ago.
Yes
Customer: replied 7 months ago.
I just want a simple quick understanding
Expert:  Ryan replied 7 months ago.
Ok, no problem. I'm not sure what material you have covered in your course, nor am I completely sure about how you are supposed to fit your particular curve into the discussion, but hopefully the following will help as a starting point. We can continue to discuss the topic after you read the following: With respect to a graph, a derivative is the slope of the tangent line to the graph at a particular point. Points on the graph where the derivative is positive indicate growth. The positive derivative means that the tangent line is sloping upward going from left to right across the graph, which means that the points on the graph are increasing in the vertical direction. Points on the graph where the derivative is small (that is, close to 0) indicate that growth is stalled and the function value (market share in the case of your particular graph) has leveled off and is remaining more or less constant. The slope of the tangent line to the graph in these areas is close to horizontal, which means that the points on the graph are not changing very much in the vertical direction. The graph in this region will appear to be "flat". And points on the graph where the derivative is negative represent decline. For these points, the slope of the tangent line is negative, which means that the tangent line is sloping downward as you move from left to right across the graph. The points on the graph will be decreasing in the vertical direction in this region, which means that the function is declining. While both curves in your graph have some of each type of point, it is not particularly helpful to zone in on any one particular point. It is a general trend that is important. For instance, looking at the blue line, the trend is generally positive (growth) for the first 26 or 27 days. Even though there are a few small dips in there, overall the derivatives in this region are positive, and the curve shows growth. From around day 29 to around day 39, the trend is mostly downward, with a little bit of "up". This is somewhat the reverse of the earlier portion of the graph. Even though there is some short-term growth in this interval, the trend is mostly a decline. Most of the derivatives in this interval would be negative. Let me know if that all makes sense to you, and please feel free to ask if you need more information or any clarification. Thanks, Ryan
Customer: replied 7 months ago.
Awesome, thank you! This helps me more than you know!
Expert:  Ryan replied 7 months ago.
You're quite welcome. If there is anything else that I can do to help, please don't hesitate to ask. Regards, Ryan