Question

The tangent to the curve $y=x^3+1$ at (1, 2) makes an agnle $\theta$ with y axis, then the value of tan $\theta$ is.

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

Answer 1

The correct option is D $-3$

Given curve is $y=x^3+1$

Differentiate it

$\Rightarrow \frac{dy}{dx}=3x^2+0=3x^2$

Thus slope of tangent to the curve at the point $(1,2)$ is

$=\frac{dy}{dx}{|}_{x=1}=3(1{)}^2=3$

If line makes an angle $\theta$ with y-axis then it will make angle $\pi -\theta$ with positive x-axis

Thus slope $=\tan (\pi -\theta )=3$

$\Rightarrow \tan \theta =-3$