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Calculus I (Practice Problems) / Applications of Derivatives / The Shape of a Graph, Part II   [Notes] [Practice Problems] [Assignment Problems]

Calculus I - Practice Problems
Derivatives Previous Chapter   Next Chapter Integrals
The Shape of a Graph, Part I Previous Section   Next Section The Mean Value Theorem

1. The graph of a function is given below.  Determine the open intervals on which the function is concave up and concave down.   

[Solution]

 

2. Below is the graph the 2nd derivative of a function.  From this graph determine the open intervals in which the function is concave up and concave down.

 

[Solution]

 

For problems 3  8 answer each of the following.

(a) Determine a list of possible inflection points for the function.

(b) Determine the open intervals on which the function is concave up and concave down.

(c) Determine the inflection points of the function.

 

3.  [Solution]

 

4.  [Solution]

 

5.  [Solution]

 

6.  on  [Solution]

 

7.  [Solution]

 

8.  [Solution]

 

For problems 9  14 answer each of the following.

(a) Identify the critical points of the function.

(b) Determine the open intervals on which the function increases and decreases.

(c) Classify the critical points as relative maximums, relative minimums or neither.

(d) Determine the open intervals on which the function is concave up and concave down.

(e) Determine the inflection points of the function.

(f) Use the information from steps (a)  (e) to sketch the graph of the function.

 

9.   [Solution] 

 

10.  [Solution]  

 

11.  [Solution] 

 

12.  on  [Solution] 

 

13.  [Solution]  

 

14.  on  [Solution] 

 

15. Determine the minimum degree of a polynomial that has exactly one inflection point. [Solution]

 

16. Suppose that we know that  is a polynomial with critical points ,  and .  If we also know that the 2nd derivative is .  If possible, classify each of the critical points as relative minimums, relative maximums.  If it is not possible to classify the critical points clearly explain why they cannot be classified. [Solution]

 

Problem Pane
The Shape of a Graph, Part I Previous Section   Next Section The Mean Value Theorem
Derivatives Previous Chapter   Next Chapter Integrals

Calculus I (Practice Problems) / Applications of Derivatives / The Shape of a Graph, Part II    [Notes] [Practice Problems] [Assignment Problems]

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