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5. (16 pts) DO NOT USE GRAPHS TO JUSTIFY YOUR ANSWER! NO CREDIT WITHOUT WORK ! Let f (x) = 5 + x ln x (a) (8 pts) Find the critical points of f. (b) (8 pts) Find the absolute minimum and the absolute maximum values of f on the interval [1, e]. Justify your answer!
5. (16 pts) DO NOT USE GRAPHS TO JUSTIFY YOUR ANSWER! NO CREDIT WITHOUT WORK! Let f (x) = x*- 8 x² +10. (a) (8 pts) Find the critical points of f. (b) (8 pts) Find the absolute maximum and absolute minimum values off on the interval (-3, 1]. Justify your answer!
6. (14 pts) EXPLANATION IS NOT REQUIRED, AND NO PARTIAL CREDIT WILL BE GIVEN. The graph of f'(derivative of f) on the interval [-6, 7] is shown in the figure. y f(x) y = f'(x) -6 -5 -4 -3 2 L - 2 3 4 5 7 Use the given graph of f' to answer the following questions about f: (a) (2 pts) on what interval (or intervals) is f decreasing? (b) (3 pts) Find the critical points of f. (c) (2 pts) which critical points (or point) correspond to local maxima ? (d) (2 pts) which critical points (or point) correspond to neither local maxima nor local minima ? (e) (2 pts) on what interval (or intervals) is f concave up? (f) (3 pts) At what point (or points) does f have an inflection point ?
