Consider the following function. f(x) = 1 ? x2/3 Find f(?1) and f(1). f(?1) = f(1) =
Question:
Consider the following function.
f(x) = 1 ? x2/3
Find f(?1) and f(1).
f(?1) =
f(1) =
Find all values c in (?1, 1) such that f?'(c) = 0. (Enter youranswers as a comma-separated list. If an answer does not exist,enter DNE.)
c =
Based off of this information, what conclusions can be madeabout 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, and0 is in the interval (?1, 1).
This contradicts Rolle's Theorem, since f(?1) = f(1), thereshould exist a number c in (?1, 1) such that f?'(c) = 0.
This does not contradict Rolle's Theorem, since f?'(0) does notexist, and so f is not differentiable on (?1, 1).
Nothing can be concluded.
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi