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