Let $f\left( {\frac{{x + y}}{2}} \right) = \frac{{f(x) + f(y)}}{2}$ and $f'(0) = a{\rm{ \,\,and}}\,\,\,{\rm{ }}f(0) = b.$ Find $f''(x)$ (where $y$ is independent of $x$), when $f(x)$ is differentiable.

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Let

f\left( {\frac{{x + y}}{2}} \right) = \frac{{f(x) + f(y)}}{2}

and

f'(0) = a\mathrm{ \,\,and}\,\,\,\mathrm{ }f(0) = b.

Find

f''(x)

(where

y

is independent of

x

), when

f(x)

is differentiable.

View answer and explanation

Correct option: A

Option A (0) is correct because the second derivative of f(x) is 0, indicating that f(x) is a linear function.

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