MHT CET · Maths · Application of Derivatives
If the normal to the curve \(y=\mathrm{f}(x)\) at the point (3,4) makes an angle of \(\left(\frac{3 \pi}{4}\right)\) with the positive X -axis, then the value of \(\mathrm{f}^{\prime}(3)\) is
- A -1
- B \(-\frac{3}{4}\)
- C \(\frac{4}{3}\)
- D 1
Answer & Solution
Correct Answer
(D) 1
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Slope of the normal }=\frac{-1}{\frac{\mathrm{~d} y}{\mathrm{~d} x}} \\ & \Rightarrow \tan \frac{3 \pi}{4}=\frac{-1}{\left(\frac{\mathrm{~d} y}{\mathrm{~d} x}\right)_{(3,4)}} \\ & \Rightarrow\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)_{(3,4)}=\mathrm{i} \\ & \Rightarrow \mathrm{f}^{\prime}(3)=1\end{aligned}\)
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