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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 \(f^{\prime}(3)=\)

  1. A \(3\)
  2. B \(2\)
  3. C \(1\)
  4. D \(4\)
Verified Solution

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 \(-\frac{1}{f^{\prime}(3)}=\tan \left(\frac{3 \pi}{4}\right)=-1\) \[ =f^{\prime}(3)^{\prime}=1 \]