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JEE Main 2005
Exam
JEE Main
Year
2005
Subject
Mathematics
Chapter
Differentiation

JEE Main 2005 · Mathematics · Differentiation

Suppose f(x) is differentiable x=1 and _ h arrow 0 (1)/(h) f(1+h)=5...

Suppose f(x)f(x) is differentiable x=1x=1 and lim⁡h→01hf(1+h)=5\lim _{h \rightarrow 0} \frac{1}{h} f(1+h)=5, then f′(1)f^{\prime}(1) equals

Options

  1. A3
  2. B4
  3. C5
  4. D6

Correct answer

C. 5

Step-by-step solution

f′(1)=lim⁡h→0f(1+h)−f(1)hf^{\prime}(1)=\lim _{h \rightarrow 0} \frac{f(1+h)-f(1)}{h}; As function is differentiable so it is continuous as it is given that lim⁡h→0f(1+h)h=5\lim _{h \rightarrow 0} \frac{f(1+h)}{h}=5 and hence f(1)=0f(1)=0 Hence f′(1)=lim⁡h→0f(1+h)h=5f^{\prime}(1)=\lim _{h \rightarrow 0} \frac{f(1+h)}{h}=5 Hence (C) is the correct answer.
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