Download Quiz #9

Math 1337
Quiz #9 (Sec. 4.1 and 4.2)
Name: ________________________________________________
Please show all work on this page.
1. Find all critical numbers of f(x) = 3x4 + 20x3 – 36x2
2. Find the absolute maximum and absolute minimum value of f(x) = 6x – x2 on [1, 7].
Use the graph shown below to find where f(x) has any local maxima and any local minima.
3. Loc. Max: ______________
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4. Loc. Min: ______________
-1
1
2
3
4
5
6
5. For f(x) = 1 – x2 on [−2, 1], do the hypotheses and conclusion of Rolle’s Theorem hold?
6. Explain why not all of the hypotheses for the Mean Value Theorem hold for f ( x)  1  x on [−1, 2].
7. Find all numbers, c, that satisfies the Mean Value Theorem for f(x) = x3 on [1, 4].
For questions 8, 9, and 10, answer True (T) or False (F).
________ 8. If c is a critical number of f(x), then f ΄(c) = 0.
________ 9. If f(c) exists and f ΄(c) = 0, then c is a critical number of f(x).
________10. The absolute extrema of a continuous function on a closed interval always exist.