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# Solution - If F : [– 5, 5] → R is a Differentiable Function and If F ′(X) Does Not Vanish Anywhere, Then Prove that F (– 5) ≠ F (5). - CBSE (Arts) Class 12 - Mathematics

ConceptMean Value Theorem

#### 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).

#### 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) is differentiable on (−5, 5).

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

Is there an error in this question or solution?

#### APPEARS IN

NCERT Mathematics Textbook for Class 12 Part 1 (with solutions)
Chapter 5: Continuity and Differentiability
Q: 3 | Page no. 186

#### 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: null - Mean Value Theorem. For the courses CBSE (Arts), CBSE (Commerce), CBSE (Science)
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