Question

Find an equation of the tangent line to the graph of y = e-x2 at the point (2, 1/e4).

Answer 1

y' = -2x*e^(-x^2).

At x = 2, that the slope of the tangent line is:
y' = (-2)(2)e^[-(2)^2]
= -4e^(-4)
= -4/e^4.

tangent line is:
y - 1/e^4 = (-4/e^4)(x - 2)
y = (-4/e^4)x + 9/e^4.