Question

Find the all points on the curve

Answer 1

Step 1 :

The function is .

The tangent line of the function is horizontal, means that, the slope of the tangent line is zero.

Set slope = .

Apply formula : .

Apply power rule of derivatives : .

Step 2 :

Solve .

If , then the general solution is , where is an integer.

General solution .

If , then ,

If , then ,

If , then , and ..............

At ,

At ,

At , , and .........

The points on the graph of the function are , where is an integer.

Comments

Step 3 :

Solve .

If , then the general solution is , where is an integer.

.

If , then ,

If , then ,

If , then , and ..............

At , .

At , .

At , and .........

The points on the graph of the function are , where is an integer.

Solution :

The points on the graph of the function are and , where is an integer.