CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, 5/e chapter 4 section 4.2 #15 f(x)=x^2

Question

CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, 5/e chapter 4 section 4.2 #15 f(x)=x^2/3-1, [-8,8] determine whether rolle's theorem can be applied to f on the closed interval[a,b]. if rolles theorem can be applied/. 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.

Explanation / Answer

The function f(x) is continuous on the closed interval [-8,8] no doubt because for both a and b a. lim (X-> a or b) Exists b. f(a or b) = a finite number and c. lim (x--> a) = f(a) and lim (x--> b) = f(b) f(-8)=64/3-1 f(8)=64/3-1 f(a) = f(b) holds true Rolle's theorem can be applied and then there is some real number c in the open interval (-8,8) such that f'(c)=0 f'=2x/3=0 x=0

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