TS EAMCET · Maths · Application of Derivatives
If the normal to the curve \(y=f(x)\) at \((1,2)\) make an angle \(\frac{3 \pi}{4}\) with positive \(X\)-axis, then \(f^{\prime}(1)=\)
- A 0
- B 1
- C 2
- D 3
Answer & Solution
Correct Answer
(B) 1
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} y & =f(x) \\ \frac{d y}{d x} & =f^{\prime}(x) \\ \left(\frac{d y}{d x}\right)_{1,2} & =f^{\prime}(1) \end{aligned} \] Slope of normal \(=\frac{-1}{f^{\prime}(1)}\) \(\therefore\) Normal of curve makes an angle \(\frac{3 \pi}{4}\) with positive…
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