Question

Determine the points at which the graph of the function has a horizontal tangent line.

Answer 1

Step 1 :

The function is and the interval is .

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

Set slope = .

The function is .

Differentiate the function with respect to .

Apply formula : .

Apply power rule of derivatives : .

Apply formula : .

.

Step 2 :

Set .

Answer 2

Contd.....

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

General solution is .

If , then ,

If , then .

The value is in the interval .

At ,

At the point the graph of the function has a horizontal tangent line.

Solution :

At the point the graph of the function has a horizontal tangent line.