| 1. |
Find two positive numbers whose sum is 10 and the sum of their cubes is as small as possible.
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| 2. |
A farmer is making a rectangular yard using 300 ft of fencing. How big can the area of the yard be ?
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| 3. |
Find the largest value of the function  in the interval  .
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| 4. |
Find the absolute minimum and maximum values of  in the interval  .
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| 5. |
Determine the minimum value of the function  in the interval  .
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| 6. |
Determine the maximum value of the function  in the interval  .
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| 7. |
Determine the minimum value of the function  in the interval .
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| 8. |
Determine the minimum value of the function  in the interval  .
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| 9. |
Determine the minimum value of the function  in the interval .
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| 10. |
Find all the critical points of the function  and determine their nature.
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| 11. |
Find all the critical points of the function  and determine their nature.
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| 12. |
Find all the critical points and determine their nature for the function  .
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| 13. |
Determine for what values of  the function  concaves up.
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| 14. |
Find all the inflection points of the function  .
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| 15. |
For what values of  is the function  increasing ?
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| 16. |
For what values of is the function  decreasing ?
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| 17. |
For what values of is the function  decreasing ?
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| 18. |
For what values of is the function  increasing ?
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| 19. |
Amongst the graphs below which graph(s) has (have) an inflection point ?
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| 20. |
Amongst the graphs above which graph(s) has (have) a critical point ?
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| 21. |
Amongst the graphs below which one corresponds to the function  with  and  ?
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| 22. |
Amongst the graphs below which one corresponds to the function  with  and  ?
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| 23. |
Amongst the graphs below which one corresponds to the function with  and ?
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| 24. |
Amongst the graphs below which one corresponds to the function with  and ?
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| 25. |
Suppose two functions differentiable everywhere are related by the equation  . Suppose  . What is  ?
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| 26. |
Suppose you are inflating a balloon. Assume that at  hours its radius is changing at the rate of  inches/hour. Assume also that at hours,  inches. What is  ?
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| 27. |
Two trucks leave a depot at the same time. One is going north, the other is going west. 5 hours after the departure the speed of the first truck is  mph, the speed of the second truck is  mph. The first truck is 200 miles away from depot and the second truck is 100 miles away from the depot. How fast is the distance between the trucks changing 4 hours after the departure?
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