Stewart7e Assignment+ 4_2.pdf - Stewart7e Assignment 4.2...

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10/24/2016 Stewart7e Assignment+ 4.2 1/7 Current Score : – / 17 Due : Wednesday, October 26 2016 11:59 PM EDT 1. –/1 pointsSCalcET7 4.2.AE.005. Video Example EXAMPLE 5 Suppose that and for all values of x . How large can possibly be? SOLUTION We are given that f is differentiable (and therefore continuous) everywhere. In particular, we can apply the Mean Value Theorem on the interval . There exists a number c such that so We are given that for all x , so in particular we know that Multiplying both sides of this inequality by 3, we have so The largest possible value for is . Stewart7e Assignment+ 4.2 (Homework) Chaniqua Ranson MAC 2311, section 13 ­ Pawan Fri10:30, Fall 2016 Instructor: Pawan Gupta WebAssign f (0) = −7 f ' ( x ) ≤ 9 f (3) [0, 3] f (3) − f (0) = f ' ( c ) − 0 f (3) = f (0) + f ' ( c ) = −7 + f ' ( c ). f ' ( x ) ≤ 9 f ' ( c ) ≤ . 3 f ' ( c ) ≤ , f (3) = −7 + f ' ( c ) ≤ −7 + = . f (3)
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10/24/2016 Stewart7e Assignment+ 4.2 2/7 2. –/4 pointsSCalcET7 4.2.005. Consider the following function. Find Find all values c in (−1, 1) such that (Enter your answers as a comma­separated list. If an answer does not exist, enter DNE.) Based off of this information, what conclusions can be made about Rolle's Theorem ? This contradicts Rolle's Theorem, since f is differentiable, f (−1) = f (1), and f ' ( c ) = 0 exists, but c is not in (−1, 1). This does not contradict Rolle's Theorem, since f ' (0) = 0, and 0 is in the interval (−1, 1). This contradicts Rolle's Theorem, since f (−1) = f (1), there should exist a number c in (−1, 1) such that f ' ( c ) = 0. This does not contradict Rolle's Theorem, since f ' (0) does not exist, and so f is not differentiable on (−1, 1).
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