Problem 21

Given information

The  function is 

To find: The two points on the curve.

Step-by-step explanation

The slope of the tangent to a curve at any point a is given by the value of the first derivative of the slope at the point .

The tangent to be horizontal so the slope should be equal to 0

That is .

The cubic function is 

Differentiating equation (1) with respect to

From the theory of cubic

Here

A double root of the equation in term of

Two distinct points having the same value

The slope of satisfies the equation (1)

Solving the equation 

The value of

The two points are