NEED ANSWERED ASAP Derivatives of exponential functions

Question

Determine the coordinates of all points at which the tangent to the curve defined by y=x²e^-x is horizontal

Answer 1

Kaitlynn,

 

       Using the product rule gives dy/dx=x² *(-e^-x)+e^-x(2x)=-e^-x(-2+x)*x. This is the equation for the tangent to the original curve, the tangent is horizontal when dy/dx=0 so setting -e^-x(-2+x)*x=0 gives x=0, 2 and ∞ are the points.

 

Hope this helps

 

Jim