Question

Using an interval chart, find the location of the extreme values of the function f(x) = x^4 e^x. Leave the coordinates of your extreme values in exact form.

Answer 1

f'(x) = (x^4 + 4x^3) e^x = x^3(x+4)e^x

f'(x)=0 at x = 0, -4
so the extremes are (-4, 256/e^4), (0,0)