Question

Write the equation of a tangent to the graphs of the following curves at the indicated points
$y=x^3$ at the point $x=2$.

Answer 1

$y=x^3$

Slope of tangent=$m=\frac{dy}{dx}=3x^2$

$⟹m={3.2}^2=12$

At $x=2$

$y=x^3=8$

Now, the equation of a line passing through point $(x_o,y_o)$ and having a slope $m$ is given by-

$(y-y_o)=m(x-x_o)$

Hence-

$y-8=12(x-2)$

$⟹y=12x-16$

$y=4(3x-4)$

This is the required equation of tangent.