AP EAMCET · Maths · Application of Derivatives
The normal to the curve \(y=f(x)\) at the points \((3,4)\) makes an angle \(\frac{3 \pi}{4}\) with positive \(X\)-axis then \(f^{\prime}(3)=\)
- A \(3\)
- B \(2\)
- C \(1\)
- D \(4\)
Answer & Solution
Correct Answer
(C) \(1\)
Step-by-step Solution
Detailed explanation
\[ \text { Given, } \begin{aligned} y & =f(x) \\ d y / d x & =f^{\prime}(x) \end{aligned} \] Slope of normal at \((3,4)\) is \(-\frac{1}{f^{\prime}(3)}=\tan \left(\frac{3 \pi}{4}\right)=-1\) \[ =f^{\prime}(3)^{\prime}=1 \]
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