JEE MATHEMATICS MCQ: DIFFERENTIATION

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Suppose

f(x)

is differentiable for all

x

and

\lim\limits _{h \rightarrow 0} \frac{1}{h} f(1+h)=5

, then

f^{\prime}

(1) equals

View answer and explanation

Correct option: B

Option B (5) is correct because

f'(1) = \lim\limits_{h \to 0} \frac{{f(1 + h) - f(1)}}{h}

and given

\lim\limits _{h \rightarrow 0} \frac{1}{h} f(1+h)=5

, it implies

f(1)=0

and

f'(1)=5

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