Question

Find an equation of the tangent line to the graph of the function at the given point.

Answer 1

Step 1 :

The function is and the point is .

The slope of the tangent line is the derivative of the function at .

Apply derivative on each side with respect to x .

Apply power property of derivative : .

Apply formulas :

                       .

Slope .

Step 2 :

At the point , the slope is :

Slope of the tangent line .

Point-slope form of a line equation is .

Substitute the point and in above equation.

The tangent line equation is .

Solution :

The tangent line equation is .