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BITSAT 2012
Exam
BITSAT
Year
2012
Subject
Mathematics
Chapter
Application of Derivatives

BITSAT 2012 · Mathematics · Application of Derivatives

If the normal to the curve y=f(x) at the point (3,4) makes an angle...

If the normal to the curve y=f(x)y=f(x) at the point (3,4) makes an angle 3π/43 \pi / 4 with the positive x\mathrm{x} -axis, then \mathrmf′(3)=\mathrmf^{\prime}(3)=

Options

  1. A-1
  2. B−3/4-3 / 4
  3. C4/34 / 3
  4. D1

Correct answer

D. 1

Step-by-step solution

Slope of normal to y=f(x)y=f(x) at (3,4) is −1f′(3)\frac{-1}{f^{\prime}(3)}.  Thus, \text{ Thus, }−1f′(3)=tan⁡(3π4)=tan⁡(π2+π4)=−cot⁡π4=−1⇒f′(3)=1\begin{array}{c} \frac{-1}{\mathrm{f}^{\prime}(3)}=\tan\left(\frac{3 \pi}{4}\right)=\tan\left(\frac{\pi}{2}+\frac{\pi}{4}\right) \\ =-\cot \frac{\pi}{4}=-1 \Rightarrow \mathrm{f}^{\prime}(3)=1 \end{array}$$
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