Question

If the normal to the curve $y=f\left(x\right)$ at the point $(3,4)$ make an angle $\frac{3\pi }{4}$ with the positive x-axis, then $f^{\prime }\left(3\right)$ is

• A. $1$
• B. $-1$
• C. $-\frac{3}{4}$
• D. $\frac{3}{4}$

Answer 1

The correct option is A $1$

$\frac{dy}{dx}=f^{\prime }\left(x\right)$, slope of normal
$=-\frac{1}{f^{\prime }\left(x\right)},-\frac{1}{f^{\prime }\left(3\right)}$
$=tan\frac{3\pi }{4}=-1$
$f^{\prime }\left(3\right)=1$