Question Bank - Mathematics

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If f : [-6, 6] \(\rm \rightarrow \) R is differentiable function and if f' (x) does not vanish anywhere, then choose which of the following option is correct.

A.
f (6) \(\rm \neq \) 0
B.
f (-6) \(\rm \neq \) 0
C.
f (-6) \(\rm \neq \) f (6)
D.
f (-6) = f (6)

Solution:

Explanation:As per Rolle's Theorem,(i) f (x) is continuous(ii) f (x) is differentiable(iii) f (a) = f (b)Then, f' (c) = 0, c \(\rm \epsilon\) (a, b)It is given f (x) is continuous and differentiable but f' (c) \(\rm \neq \) 0f (a) \(\rm \neq \) f (b)f (-6) \(\rm \neq \) f (6)

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