#### Question

If f : [– 5, 5] → R is a differentiable function and if f ′(x) does not vanish anywhere, then prove that f (– 5) ≠ f (5).

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#### Solution

It is given that f : [– 5, 5] → R is a differentiable function.

Since every differentiable function is a continuous function, we obtain

(a) *f* is continuous on [−5, 5].

(b) *f *is differentiable on (−5, 5).

Therefore, by the Mean Value Theorem, there exists *c* ∈ (−5, 5) such that

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#### Reference Material

Solution for question: If F : [– 5, 5] → R is a Differentiable Function and If F ′(X) Does Not Vanish Anywhere, Then Prove that F (– 5) ≠ F (5). concept: Mean Value Theorem. For the courses CBSE (Arts), CBSE (Commerce), CBSE (Science)