Question

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

y = e^2x cos πx,       (0, 1)

Answer 1

Step 1:

The function is and point is .

Apply derivative on each side with respect to .

Use product rule : .

Substitute in above expression.

.

Slope of a tangent line is .

Step 2:

Point - slope form of a line equation is .

Substitute and in point - slope form.

Solution :

The tangent line equation is .