Question

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.

Answer 1

Step 1:

The functions are and , .

Consider .

Apply derivative on each side with respect to .

Consider .

Apply derivative on each side with respect to .

Step 2:

Find .

Substitute the values of in above expression.

Step 3:

Find slope of the tangent at .

Substitute in .

.

Slope of a tangent line is .

Find the point corresponding to the value .

Substitute in .

Substitute in .

Now obtained point is

Point - slope form of a line equation is .

Substitute and in point - slope form.

The tangent line equation is .

Solution :

The tangent line equation is .