Question

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

y = x³ – x at x = 2

Answer 1

Given:

y = x³ – x at x = 2

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

\(\therefore\frac{dy}{dx}\)(xⁿ) = n.x^{n – 1}

The Slope of the tangent is \(\frac{dy}{dx}\)

⇒ y = x³ – x

\(\therefore\)The Slope of the tangent at x = 2 is 11

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

⇒ The Slope of the normal =\(\frac{-1}{(\frac{dy}{dx}x=2)}\)

⇒ The Slope of the normal =\(\frac{-1}{11}\)