Q. If the normal to the curve $y = f(x)$ at the point (3, 4) makes an angle $\frac{3\pi}{2}$ with the positive $x$-axis, then $f^{'}(3)$ is equal to
A) $- 1$
B) $- \frac{3}{4}$
C) $\frac{4}{3}$
D) 1
Explanation
(d)
Slope of the curve at an angle $\theta = \frac{3\pi}{4}$ is
$\frac{dy}{dx} = \tan\frac{3\pi}{4} = - 1$
Slope of the normal $= \frac{- 1}{dy/dx}$
$\therefore\ \ \left( \frac{dy}{dx} \right)_{(3,\ 4)} = 1$
$\Rightarrow \ \ \ f^{'}(3) = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.