Find the The Slopes of the tangent and the normal to the following curves at the indicated points : y = √x^3 at x = 4

Question

Find the The Slopes of the tangent and the normal to the following curves at the indicated points :

 \(y=\sqrt{x^3}\) at x = 4

Answer 1

Given:

\(y=\sqrt{x^3}\) at x = 4

First, we have to find \(\frac{dy}{dx}\) of given function, f(x),i.e, to find the derivative of f(x)

\(y=\sqrt{x^3}\)

\(\therefore\)The Slope of the tangent at x = 4 is 3

⇒ The Slope of the normal = \(\frac{1}{\text{The Slope of the tangent}}\)

⇒ The Slope of the normal = \(\frac{-1}{(\frac{dy}{dx}x=4)}\)

⇒ The Slope of the normal = \(\frac{-1}{3}\)