Question

Find the tangent line to the curve y= e^(2-x^2) when x = 1.

Answer 1

let 2-x^2=u -> y'=e^udu -> du = -2x -> y'=-2xe^(2-x^2)
slope of the tangent line is -2e^2
now find a few points on the line and write the line's equation.

Answer 2

y = -2ex + 3e

the slope is actually -2e, right? becayse e^(2-1^2)=e

Answer 3

Yes, the slope is \(-2e\).