Question

If the tangent to the function $y = f(x) $ at $(3,4)$ makes an angle of $\frac{3 \pi }{4}$ with the positive direction of x-axis in anticlockwise direction then $f ' (3)$ is

• A. $-1$
• B. $1$
• C. $\frac{1}{\sqrt{3}}$
• D. $\sqrt{3}$

Answer 1

Answer: (A)

Given $y = f ( x )$
Differentiating w.r.t $x$,
we get $y'=f'(x)$
which is the slope of the tangent
$f'(3)=\tan \frac{3 \pi}{4}=-\tan \frac{\pi}{4}=-1$
Hence, $f'(3)=-1$.