Question

If the normal to the curve $y = f(x)$ at $(3,4)$ 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. 1
• D. $- \frac{3}{4}$

Answer 1

Answer: (C)

1

Answer 2

Slope of the normal at (3,4) is the value of $- \frac{1}{f'\left(x\right)}$ at $x=3$ or $- \frac{1}{f'\left(3\right)} = \tan \frac{3\pi}{4} = - 1$
$\Rightarrow f'\left(3\right) = 1$