(2) Suppose f: RR is twice differentiable, i.e., f' is a differentiable function. Suppose that a, h ER and h> 0. Show that there exists c = (a - h, a + h) such that f(a+h)-2f(a) + f(a - h) Hint: Let g(x) g' (b) f" (c) ƒ (x) − ƒ (x − h) h g(b+h) – g(b) h h² and show that there is a b E (a, a + h) with
(2) Suppose f: RR is twice differentiable, i.e., f' is a differentiable function. Suppose that a, h ER and h> 0. Show that there exists c = (a - h, a + h) such that f(a+h)-2f(a) + f(a - h) Hint: Let g(x) g' (b) f" (c) ƒ (x) − ƒ (x − h) h g(b+h) – g(b) h h² and show that there is a b E (a, a + h) with
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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