Question

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

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

Answer 1

Answer: (A)

$-1$

Given $y=f\left(x\right)$

Differentiating w.r.t x, we get

$y^{\prime }=f^{\prime }\left(x\right)$ which is the slope of the tangent

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

Hence, $f^{\prime }\left(3\right)=-1$.