3 At what po?ints c? does the conclusion of the Mean Value Theorem hold ? f?or?? ) = x on the interval [?10,10]?
Solution 6E Step 1 In this problem we have to find the value of c for which the conclusion of the mean value theorem for f(x) = x holds on the interval [-10,10] Mean Value theorem: If f is defined and continuous on the closed interval [a,b]and differentiable on the open interval (a,b)then there is at least one point cin (a,b)that is f(b) f(a) a < c < bsuch that f(c) = ba Step 2 3 Given that f(x) = x is defined on [-10,10] Since f is a polynomial, f is continuous and differentiable everywhere. Hence f is continuous in the closed interval [-10,10] and differentiable in the open interval (-10,10). Thus f satisfies all the conditions of mean value theorem on the given interval [-10,10]. Therefore by Mean value theorem, there is at least one point cin (-10,10) such f(10) f(10) that f(c) = 10+10 … ( 1)
Textbook: Calculus: Early Transcendentals
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
The full step-by-step solution to problem: 6E from chapter: 4.6 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The answer to “3 At what po?ints c? does the conclusion of the Mean Value Theorem hold ? f?or?? ) = x on the interval [?10,10]?” is broken down into a number of easy to follow steps, and 23 words. Since the solution to 6E from 4.6 chapter was answered, more than 315 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This full solution covers the following key subjects: conclusion, hold, interval, ints, mean. This expansive textbook survival guide covers 85 chapters, and 5218 solutions.