create test paper on the basis of rolle,s theorem

Consider the following function.f(x) = 1 − x2/3Find f(−1) and f(1).f(−1)= 0 f(1)= 0 Find all values c in (−1, 1) such that f '(c) = 0. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)c = 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).Nothing can be concluded.

Generate a test paper based on your lecture slides

Generate a test paper based on your lecture slide

Rolle's Theorem is valid for the given function f(x)=x3+bx2+cx,1≤x≤2 at the point x= 43, then values of b and c are respectively

enerate a test paper based on your lecture slid