Question

Find an equation of the tangent line to the curve

Answer 1

Step 1:

The curve is

Differentiate on each side with respect to .

Apply product rule in derivatives

is slope of the tangent line.

Step 2:

The tangent line is parallel to .

Write the equation in slope intercept form , where is slope and is -intercept.

Parallel lines have equal slope.

Using the - value find the corresponding - value with the curve.

Therefore tangent point is.

Step 3:

Find the tangent line equation, substitute the values of and in the slope intercept form of an equation .

Substitute and in .

Solution :

Tangent line is .