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

Question

Find the The Slopes of the tangent and the normal to the following curves at the indicated points : y = x 3 – x at x = 2

Philoid · Accepted Answer

Given:

y = x³ – x at x = 2

First, we have to find of given function, f(x),i.e, to find the derivative of f(x)

(xⁿ) = n.x^{n – 1}

The Slope of the tangent is

⇒ y = x³ – x

(x³) + 3(x)

= 3.x^{3 – 1} – 1.x^{1 – 0}

= 3x² – 1

Since, x = 2

_{x = 2} = 3(2)² – 1

_{x = 2} = (34) – 1

_{x = 2} = 12 – 1

_{x = 2} = 11

The Slope of the tangent at x = 2 is 11

⇒ The Slope of the normal =