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

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

For problems 1 and 2 use the graph of the function, , estimate the value of  for the given values of a.

 

1.    (a) (b)  

 

[Solution]

 

2.    (a)     (b)  

 

[Solution]

 

For problems 3 and 4 sketch the graph of a function that satisfies the given conditions.

 

3. , , ,  [Solution]

 

4. , , , , ,  [Solution]

 

For problems 5 and 6 the graph of a function, , is given.  Use this to sketch the graph of the derivative, .

 

5.

[Solution]

 

6.

[Solution]

7. 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?

[Solution]

8. What is the equation of the tangent line to  at . [Solution]

 

9. 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 yes, at what time(s) does the object stop moving?

[Solution]

 

10. What is the equation of the tangent line to  at ? [Solution]

 

11. Determine where, if anywhere, the function  stops changing. [Solution]

 

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

      (a)  

      (b)  

      (c)  

[Solution]

 

13. 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 yes, at what times(s) does the volume stop changing?

[Solution]

 

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

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

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