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Calculus I (Assignment Problems) / Derivatives / Interpretation of the Derivative   [Notes] [Practice Problems] [Assignment Problems]

Calculus I - Assignment Problems
Limits Previous Chapter   Next Chapter Applications of Derivatives
The Definition of the Derivative Previous Section   Next Section Differentiation Formulas

 Interpretations of the Derivative

For problems 1  3 use the graph of the function, , estimate the value of  for the given values of a.

 

1.    (a) (b)  

 

 

2.    (a) (b)  

 

 

3.    (a) (b)  

 

 

For problems 4  6 sketch the graph of a function that satisfies the given conditions.

 

4. , , ,  

 

5. , , ,  

 

6. , , , , ,  

 

For problems 7  9 the graph of a function, , is given.  Use this to sketch the graph of the derivative, .

 

7.

 

8.

 

9.

 

10. Answer the following questions about the function .

    (a) Is the function increasing or decreasing at ?

    (b) Is the function increasing or decreasing at ?

    (c) Does the function ever stop changing?  If yes, at what value(s) of z does the  

          function stop changing?

 

11. What is the equation of the tangent line to  at .

 

12. The position of an object at any time t is given by .

    (a) Determine the velocity of the object at any time t.

    (b) Is the object moving to the right or left at ?

    (c) Is the object moving to the right or left at ?

    (d) Does the object ever stop moving?  If so, at what time(s) does the object stop

          moving?

 

13. Does the function  ever stop changing?  If yes, at what value(s)

      of w does the function stop changing?

 

14. Suppose that the volume of air in a balloon for  is given by  .

      (a) Is the volume of air increasing or decreasing at ?

      (b) Is the volume of air increasing or decreasing at ?

      (c) Does the volume of air ever stop changing?  If yes, at what times(s) does the

           volume stop changing?

 

15. What is the equation of the tangent line to  at ?

 

16. Answer the following questions about the function .

    (a) Is the function increasing or decreasing at ?

    (b) Is the function increasing or decreasing at ?

    (c) Does the function ever stop changing?  If yes, at what value(s) of x does the 

          function stop changing?

 

17. Determine if the function  increasing or decreasing at the given points.

      (a)  

      (b)  

      (c)  

 

18. Suppose that the volume of water in a tank for  is given by  .

      (a) Is the volume of water increasing or decreasing at ?

      (b) Is the volume of water increasing or decreasing at ?

      (c) Does the volume of water ever stop changing?  If so, at what times(s) does the

           volume stop changing?

 

19. What is the equation of the tangent line to  at ?

 

20. The position of an object at any time t is given by .

    (a) Determine the velocity of the object at any time t.

    (b) Does the object ever stop moving?  If so, at what time(s) does the object stop

          moving?

 

21. Does the function  ever stop changing?  If yes, at what value(s)

      of t does the function stop changing?

The Definition of the Derivative Previous Section   Next Section Differentiation Formulas
Limits Previous Chapter   Next Chapter Applications of Derivatives

Calculus I (Assignment Problems) / Derivatives / Interpretation of the Derivative    [Notes] [Practice Problems] [Assignment Problems]

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