JEE Main & Advanced Mathematics Limits, Continuity and Differentiability Question Bank Self Evaluation Test - Continuity and Differentiability

  • question_answer
    Suppose \[f(x)\] is differentiable at \[x=1\] and \[\underset{h\to 0}{\mathop{\lim }}\,\frac{1}{h}f(1+h)=5\] then \[f'(1)\] equals

    A) 3

    B) 4

    C) 5

    D) 6

    Correct Answer: C

    Solution :

    [c] \[f'(1)=\underset{h\to 0}{\mathop{\lim }}\,\frac{f(1+h)-f(1)}{h};\] As function is differentiable so it is continuous as it is given that \[\underset{h\to 0}{\mathop{\lim }}\,\frac{f(1+h)}{h}\] = 5 and hence \[f(1)=0\] Hence \[f'(1)=\underset{h\to 0}{\mathop{\lim }}\,\frac{f(1+h)}{h}=5\]


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