Question

The graph y=(x+2)e^(x^2/2) has one horizontal tangent line. What is the equation of this tangent line?

Answer 1

Assuming that e^[(x^2)/2]

lets compute the derivative:

y'= exp (x^2/2).(x+1)^2

when y'=o then we have a horizontal line, thus

x = -1 so y =1,64 approximately

the equation of a horizontal line is the y axes, so the answer is y=1,64

Answer 2

why is it (x+1)^2? I don't get it.