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Find an equation of the...

Find an equation of the tangent line at the indicated point on the graph of the function.

1. s=h(t)=t^3-9t+5 (t,s)=(3,5)

Find the derivative

2. f(x)= (4)/(√x)-(6)/(x)+(8)/(x)^4

3. If the price of a product is given by P(x)=(1024)/(x) +1200, where x represents the demand for the product, find the rate of change of price when the demand is 8.

4. Find the first and second derivatives of the function g(t)=(4t-5)^3/2.

5. Sketch the graph of the function, indicating all critical points and inflection points. Apply the second derivative test at each critical point. Show the correct concave structure.

6. Sketch the graph of f(x). Identify all extrema, inflection points, intercepts and asymptotes. Show the concave structure clearly and note any discontinuities.

f(x)=(x^2)/(x-1)

7. The driver of a car traveling at 60 ft/sec suddenly applies the brakes. The position of the car is s=60t-3t^2, t seconds after the driver applies the brakes.How many seconds after the driver applies the brakes does the car come to a stop?

Find the derivative

8. y=(e^-x+1) / (e^x)

Find the derivative of the function.

9. y=ln(7+x^2)

10. Given the function y=[(1+2x)^3/2)] / [(1+3x)^4/3], find dy/dx by logarithmic differentiation.

11. A certain radioactive element has a half-life of 12 minutes. At what time is the substance decaying at a rate of 3.466 grams per minute if there are 120 grams present initially?

1. s=h(t)=t^3-9t+5 (t,s)=(3,5)

Find the derivative

2. f(x)= (4)/(√x)-(6)/(x)+(8)/(x)^4

3. If the price of a product is given by P(x)=(1024)/(x) +1200, where x represents the demand for the product, find the rate of change of price when the demand is 8.

4. Find the first and second derivatives of the function g(t)=(4t-5)^3/2.

5. Sketch the graph of the function, indicating all critical points and inflection points. Apply the second derivative test at each critical point. Show the correct concave structure.

6. Sketch the graph of f(x). Identify all extrema, inflection points, intercepts and asymptotes. Show the concave structure clearly and note any discontinuities.

f(x)=(x^2)/(x-1)

7. The driver of a car traveling at 60 ft/sec suddenly applies the brakes. The position of the car is s=60t-3t^2, t seconds after the driver applies the brakes.How many seconds after the driver applies the brakes does the car come to a stop?

Find the derivative

8. y=(e^-x+1) / (e^x)

Find the derivative of the function.

9. y=ln(7+x^2)

10. Given the function y=[(1+2x)^3/2)] / [(1+3x)^4/3], find dy/dx by logarithmic differentiation.

11. A certain radioactive element has a half-life of 12 minutes. At what time is the substance decaying at a rate of 3.466 grams per minute if there are 120 grams present initially?

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