What is the slope of the line tangent to the graph of f(x)=-2x/e^x at x=-3?

Answer 1

f(x) = -2x / e^x

f'(x) = [-2e^x + -2xe^x] / e^2x

Slope of tangent line = f'(-3) = 4e^-3 / e^-6 = 4e³

Point on tangent line = (-3, f(-3)) = (-3, 6e³)

Equation of tangent line: y - 6e³ = 4e³(x + 3)

So y = 4e³x + 18e³