Question

Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. If so, find all values of c in the open interval (a,b) such that $f'(c) = 0$. If Rolle's Theorem cannot be applied, explain why not. 1. $f(x) = x(x-1)^3$, $[0,1]$ 2. $f(x) = 5 - 12x - 2x^2$, $[-7,1]$

          Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b].
If so, find all values of c in the open interval (a,b) such that $f'(c) = 0$. If Rolle's
Theorem cannot be applied, explain why not.
1. $f(x) = x(x-1)^3$, $[0,1]$
2. $f(x) = 5 - 12x - 2x^2$, $[-7,1]$

Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b].
If so, find all values of c in the open interval (a,b) such that f'(c) = 0. If Rolle's
Theorem cannot be applied, explain why not.
1. f(x) = x(x-1)^3, [0,1]
2. f(x) = 5 - 12x - 2x^2, [-7,1]

Added by Dana A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Kathleen Carty

Step 1

For the function f(x) = x(x-1) on the closed interval [0,1], we can check if Rolle's Theorem can be applied by verifying the conditions: - f(x) is continuous on [0,1]: Yes, f(x) = x(x-1) is a polynomial function and is continuous on the interval [0,1]. - f(x) is Show more…

Show all steps

Thanks for your feedback!

Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. If so, find all values of c in the open interval (a, b) such that f(c) = 0. If Rolle's Theorem cannot be applied, explain why not. 1. f(x) = x(x-1) [0,1] 2. f(x) = 5-12x-2x^2 [-7,1]