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Unformatted text preview: 4. (10 points) Consider the function f ( x ) = 2 3 x 35 x 2 + 12 x . (a) Find all intervals where f is increasing. (b) Find all intervals where f is decreasing. (c) Find all intervals where f is concave up. (d) Find all intervals where f is concave down. (e) Find all inﬂection points of f ( x ). 5. (10 points) Suppose that f ( x ) is a twicediﬀerentiable function and that the graph of y = f ( x ) is shown below. L M 3, M 1 R L 2, M 1 R y E f L x R (a) Which of the following best describes the value of f (0)? A. It is positive. B. It is negative. C. It is zero. D. Its sign cannot be determined from the graph. (b) Which of the following best describes the value of f 00 (3)? A. It is positive. B. It is negative. C. It is zero. D. Its sign cannot be determined from the graph. (c) How many inﬂection points does f have in the interval [3 , 2]?...
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 Spring '08
 Hotlz
 Math, Calculus, Derivative, Mathematical analysis, Convex function, a. b. c., b. c. d.

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