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MAT-1110 Midterm: MATH 1110 App State summer2012 Test2 answer key

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turquoisegnu128

15 Feb 2019

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Name: answer key: (15 points) let f (x) = 2x3 6x2 + 18x 5 (a) find the critical points of f (x). Decide if each of these points is a local minimum, a local maximum, or neither. Notice that f (x) = 6x2 12x + 18 is de ned everywhere, so our only critical points come from solutions of f (x) = 0. We can factor this quadratic to nd the solutions: f (x) = 6x2 12x + 18 = 6(x2 + 2x 3) = So the critical points are located at x = 3 and 1. So this is a local minimum. f (1) = 12(1) 12 = 24 < 0 so f is concave down at x = 1. Answer: x = 3 is a local minimum and x = 1 is a local maximum. (b) find the maximum and minimum value of f (x) restricted to the interval [0, 2].

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