MATH 221 Midterm: MATH 221 UW Madison Exam4
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Show all work and explain your answer: find all critical points of the function f (x) = x. 5 (x 4)2: (a) verify that f (x) = 2x3 + x2 x 1 satis es the hypotheses of the. Mean value theorem on the interval [0, 2]. (b) find all numbers c that satisfy the conclusion of the mean value. Theorem: find all intervals where f (x) = x4 8x2 + 1 is (a) increasing (b) decreasing (c) concave up (d) concave down, graph f (x) = ln(x) x . If the perimeter of the window is 30 nd the dimensions of the window so that the greatest possible amount of light is admitted: find the most general antiderivative of f (x) = x2 + 1 x. 2. (4. 2-12) (a) any polynomial is di erentiable and continuous every- is the only solution of f (c) = 9 in the b a = 9, c = 1+ 61.
