B. Johnson

Calculus Worksheet Ch 3 – Derivative Test Review

1. Use the definition of the derivative to find the derivative of the following.

a) b) c)

2. Find values of x where has horizontal tangents.

3. Evaluate

4. Let . The tangent to at intersects again for what value(s) of x?

5. Find the point of the graph of between and , where the slope of the tangent line equals

the slope of the secant line from to .

6. Find m and n such that f will be differential at .

7. For what value(s) of x will the tangent lines to be perpendicular to ?

8. Approximate using a tangent line approximation (linear approximation).

9. Find an equation of a line tangent to that is parallel to .

10. If and when and , find .

11. Water is flowing at the rate of into a tank in the form of an inverted cone having an altitude of 16 meters and a radius of 4 meters. a) How fast is the water level rising when the water is 5 meter deep? Indicate units. b) How ling would it take to fill the tank?

12. If , then

A. B. C. 4 D. E. 8

13. An equation of the line tangent to the graph of at the point is

A. B. C. D. E.

14. What is the instantaneous rate of change at of the function f given by ?

A. B. C. D. 2 E. 6

15. If , what is the value of at the point ?

A. B. C. D. E.