Question

Given the function f(x)= e^2x(x^2-2)

a. does the decreasing arc reach a local or global minimum?

b. does f have a global max?

Answer 1

f = e^2x(x^2-2)
f ' = 2e^2x(x-1)(x+2)
f '' = 2e^2x(2x^2+4x-3)

f'=0 at x=-1,2
f''(-2) < 0, so a max at x = -1
f''(1) > 0, so a min at x=2

Since f(x) --> 0 as x --> -oo, the minimum is a global min.

since f(x) --> +oo as x --> +oo, there is no global max

Answer 2

yo do your own hw headass

Answer 3

Honestly