Question

Find the equation of the tangent at origin to the curve $y=x^{\frac{3}{2}}$.

Answer 1

Given the curve $y=x^{\frac{3}{2}}$.

Now $\frac{dy}{dx}=\frac{3}{2}{x}^{\frac{1}{2}}$.

Now,${\frac{dy}{dx}|}_{(0,0)}=0$.

So the equation of tangent at $(0,0)$ to the given curve is

$(y-0)=$${\frac{dy}{dx}|}_{(0,0)}$ $(x-0)$

or, $y=0$.