If f(2+x)=f(−x) for all x∈R, then differentiable at x = 4 implies differentiability at x=

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If $f (2 + x) = f (- x) f o r a l l x \in R,$ then differentiable at x = 4 implies differentiability at x=

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answer is -2.

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Detailed Solution

$f (2 + x) = f (- x)$

Replacing x by x - 1, we get

$f (2 + x - 1) = f (- x + 1) o r f (1 + x) = f (1 - x)$

Hence, f(x) is symmetrical about line x = 1.

Now, putting x = 2 in (1), we get f(4) = f(-2). Hence,

differentiable at x = 4 implies differentiability at x = -2.

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