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Calculus I (Assignment Problems) / Applications of Derivatives / Minimum and Maximum Values   [Notes] [Practice Problems] [Assignment Problems]

Calculus I - Assignment Problems
Derivatives Previous Chapter   Next Chapter Integrals
Critical Points Previous Section   Next Section Finding Absolute Extrema

 Minimum and Maximum Values

 

1. Below is the graph of some function,  .  Identify all of the relative extrema and absolute extrema of the function.

 

2. Below is the graph of some function,  .  Identify all of the relative extrema and absolute extrema of the function.

 

3. Below is the graph of some function,  .  Identify all of the relative extrema and absolute extrema of the function.

 

4. Below is the graph of some function,  .  Identify all of the relative extrema and absolute extrema of the function.

 

5. Sketch the graph of  and identify all the relative extrema and absolute extrema of the function on each of the following intervals.

(a)  

(b)   

(c)  

(d)  

 

6. Sketch the graph of  and identify all the relative extrema and absolute extrema of the function on each of the following intervals.

(a)  

(b)   

(c)  
            (d)   

(e)  

            (f)    

 

7. Sketch the graph of  and identify all the relative extrema and absolute extrema of the function on each of the following intervals.

(a)  

(b)   

(c)  

(d)  

 

8. Sketch the graph of  and identify all the relative extrema and absolute extrema of the function on each of the following intervals.  Do, all work for this problem in radians.

(a)  

(b)   

(c)  

(d)   

 

9. Sketch the graph of a function on the interval  that has an absolute maximum at  and an absolute minimum at .

 

10. Sketch the graph of a function on the interval  that has an absolute minimum at  and an absolute maximums at  and  .

 

11. Sketch the graph of a function on the interval  that has a relative minimum at , a relative maximum at  and no absolute extrema.

 

12. Sketch the graph of a function that meets the following conditions :

(a) Has at least one absolute maximum.

(b) Has one relative minimum.

(c) Has no absolute minimum.

 

13. Sketch the graph of a function that meets the following conditions :

(a) Graphed on the interval .

(b) Has a discontinuity at some point interior to the interval.

(c) Has an absolute maximum at the discontinuity in part (b).

 

14. Sketch the graph of a function that meets the following conditions :

(a) Graphed on the interval .

(b) Has no relative extrema.

(c) Has an absolute maximum at one end point.

(d) Has an absolute minimum at the other end point.

 

15. Sketch the graph of a function that meets the following conditions :

(a) Has a discontinuity at some point.

(b) Has an absolute maximum and an absolute minimum.

(c) Neither absolute extrema occurs at the discontinuity.

 

Critical Points Previous Section   Next Section Finding Absolute Extrema
Derivatives Previous Chapter   Next Chapter Integrals

Calculus I (Assignment Problems) / Applications of Derivatives / Minimum and Maximum Values    [Notes] [Practice Problems] [Assignment Problems]

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