Question

If the normal to the curve y = f(x) at the point (1, –1) makes an angle $\frac{3\pi }{4}$ with positive x-axis, then f'(1) =

• A. -1
• B. 1
• C. 0.0
• D. 2

Answer 1

The correct option is B 1

Slope of normal $=\frac{-1}{f^{\prime }(x{)}_{(1,-1)}}=\frac{-1}{f^{\prime }\left(1\right)}$
But it has been given that $\frac{-1}{f^{\prime }\left(1\right)}=\tan \frac{3\pi }{4}\Rightarrow f^{\prime }\left(1\right)=1$