Find the equations of the tangent and normal to the given curves at the indicated points:

Question

Find the equations of the tangent and normal to the given curves at the indicated points: y = x 3 at (1, 1)

Philoid · Accepted Answer

It is given that equation of curve is y = x³

On differentiating with respect to x, we get

= 3x²

Therefore, the slope of the tangent at (1, 1) is 3.

Then, the equation of the tangent is

y – 1 = 3(x – 1)

⇒ y = 3x - 2

Then, slope of normal at (1,1)

=

Now, equation of the normal at (1,1)

y – 1 = (x – 1)

⇒ 3y -3 =- x + 1

⇒ x + 3y - 4 = 0