A function f(x) and interval a, b] are given. Check if the Mean Value Theorem can be applied to f on a, b]. If so, find all values c in la, b] guaranteed by the Mean Value Theorem Note, if the Mean Value Theorem does not apply, enter DNE for the c value. f(x) = 2x3 – 3x² – 72x + 10 [-6, 8] - - on c = (Separate multiple answers by commas.)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A function f(x) and interval [a, b] are given. Check if the Mean Value Theorem can be applied to f on [a, b]. If so, find all values c in
a, b guaranteed by the Mean Value Theorem
Note, if the Mean Value Theorem does not apply, enter DNE for the c value.
f(x) = 2x° – 3x? – 72x + 10
on [-6, 8]
c =
(Separate multiple answers by commas.)
Transcribed Image Text:A function f(x) and interval [a, b] are given. Check if the Mean Value Theorem can be applied to f on [a, b]. If so, find all values c in a, b guaranteed by the Mean Value Theorem Note, if the Mean Value Theorem does not apply, enter DNE for the c value. f(x) = 2x° – 3x? – 72x + 10 on [-6, 8] c = (Separate multiple answers by commas.)
Expert Solution
Step 1

Given:

fx=2x3-3x2-72x+10 ; a,b=-6,8

 

As we know from the Mean value theorem:

If f(x) is real-valued function is defined on [a, b] and

a). fx is continuous on a,b

b). fx is differentiable on a,b then there exists at least one c point in a,b such that

f'c=fb-fab-a

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