Show that Rolle's Theorem can be applied to the following functions on the closed interval [a,b], then find all values c in the open interval (a,b) for which f'(c)=0. a. f(x)=x²-x², [−–2,2] b. f(x)=sin 27x, [-1.1]
Show that Rolle's Theorem can be applied to the following functions on the closed interval [a,b], then find all values c in the open interval (a,b) for which f'(c)=0. a. f(x)=x²-x², [−–2,2] b. f(x)=sin 27x, [-1.1]
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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4. Show that Rolle's Theorem can be applied to the following functions on the closed
interval [a,b], then find all values c in the open interval (a, b) for which f'(c)=0.
a. f(x)=x²-x², [−2,2]
b. f(x)=sin 2лx, [−1,1]
4.
Answer from solution manual:
a. f is a polynomial so it is continuous and
differentiable everywhere;
f(-2)=12=f(2); c= 0,±
b. f is a sine function is continuous and
differentiable everywhere;
f(-1)=0= f(1) c = ±, ± ²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd0096572-fde0-4644-aa4e-058f46ddb927%2F0a66b9be-2cf1-4c67-b65b-61644dfd187f%2Fid17o4p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:с
4. Show that Rolle's Theorem can be applied to the following functions on the closed
interval [a,b], then find all values c in the open interval (a, b) for which f'(c)=0.
a. f(x)=x²-x², [−2,2]
b. f(x)=sin 2лx, [−1,1]
4.
Answer from solution manual:
a. f is a polynomial so it is continuous and
differentiable everywhere;
f(-2)=12=f(2); c= 0,±
b. f is a sine function is continuous and
differentiable everywhere;
f(-1)=0= f(1) c = ±, ± ²
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