If the normal to the curve y=f(x) at the point (3,4) make an angle 3 π / 4 with the positive x -axis, then f(3) is

Correct answer: (A) 1. Hints: (d y)/(d x)=f^′(x) , Slope of normal =-frac1f^′(x),-frac1f^′(3)=tan (3 π)/4=-1 f^′(3)=1

Q102 / 160 · WBJEE 2010 · Mathematics

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

Correct answer
A
1
B
-1
C
$-\frac{3}{4}$
D
$\frac{3}{4}$

Solution

Hints: $\frac{d y}{d x}=f^{\prime}(x)$, Slope of normal $=-\frac{1}{f^{\prime}(x)},-\frac{1}{f^{\prime}(3)}=\tan \frac{3 \pi}{4}=-1$ $f^{\prime}(3)=1$

Hence, the correct answer is option: 'A'.

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