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MAT-1110 Midterm: MATH 1110 App State summer2014 Test2

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turquoisegnu128

15 Feb 2019

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Show your work: (11 points) implicit di erentiation. (a) use implicit di erentiation to nd (x, y) = (1, 2). dy dx given x2 + y2 = 5. P5(x) = 5 + 3(x + 2) 2(x + 2)2 + (x + 2)5. Either ll in the blank or circle not enough info. if there isn"t enough information to nd the answer. The linearization of g(x) based at x = 2 is. Or not enough info: (10 points) use newton"s method to approximate a solution of x3 = 2. Use the initial guess x0 = 1 and work through. Use the racetrack principal to justify why this is true for x 1. [note: ln(1) = 0. ] (b) suppose f (2) = 3 and f (5) = 12 and suppose that f is di erentiable everywhere. Then the mean value theorem (mvt) guarantees that there is some c such that. f (c) = and.

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