Thread: Maxima & Minima

1) g(x) = x^2(e^-x)
(Give exact values for the coordinates of any maxima or minima. Use 3-decimal-place accuracy for inflection-point coordinates.)

-I differentiated g(x) and got g'(x)= x^2(-e^-x) + (e^-x(2x)). I am not sure how to continue the problem and am a little confused with the algebra involved. If any one knows how to do this problem, please help me. Thank you.

have:



and you differentiated wrt x to get:



we want to set the derivative to zero:



well the exponential function is never zero for x in reals so:



we have and then calculate higher derivatives of to find the nature of these turning points.