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Question

Find the value of c in a Rolle's theorem for the function f(x)=x33x in [3,0].

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Solution

Given function f(x)=x33x is a polynomial function.

f(x) is continuous as well as differentiable in [3,0].

Also, f(3)=(3)23(3)=33+33=0

And, f(0)=0 Thus, all the three conditions of Rolle's Theorem are satisfied.

There exist at least one real number c, such that f(c)=0

f(x)=3x23

3c23=0

c2=1

c=±1
Thus, c=1 (3,0)

Hence, value of c is 1.

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