Question

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

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

Answer 1

Answer: (D)

1

Answer 2

Slope of the normal $= \frac{- 1}{dy/dx}$

⇒ $\tan\frac{3\pi}{4} = \frac{- 1}{\left( \frac{dy}{dx} \right)_{(3,4)}}$

$\therefore$ $\left( \frac{dy}{dx} \right)_{(3,4)} = 1$; $f^{'}(3) = 1$.