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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]

Intermediate Algebra
Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Conic Sections
Section8.2: More Parabolas And Some Circles
Problem 63.1PS
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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
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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