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

Question

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

y = 9e^x cos(x),    (0, 9)

Answer 1

Point (0,9) is tangent point because y = f((0) = 9e⁰cos0 = 9.

To get slope of tangent line m we differentiate y' = 9e^xcosx - 9e^xsinx; m = f'(0) = 9.

Equation of tangent line: y = 9 + 9(x - 0), y = 9x + 9