WBJEE · Maths · Application of Derivatives
If the normal to the curve \(y=f(x)\) at the point \((3,4)\) make an angle \(3 \pi / 4\) with the positive \(x\)-axis, then \(f(3)\) is
- A 1
- B -1
- C \(-\frac{3}{4}\)
- D \(\frac{3}{4}\)
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
Hints: \(\frac{d y}{d x}=f^{\prime}(x)\), Slope of normal \(=-\frac{1}{f^{\prime}(x)},-\frac{1}{f^{\prime}(3)}=\tan \frac{3 \pi}{4}=-1\) \(f^{\prime}(3)=1\)
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