Question

2. f(x) = x^3×e^x. Determine the interval(s) where f(x) is increasing and decreasing. Answer in interval notation.

Answer 1

we have the function

f(x)=x^3(e^x)

using a graphing tool

graph the function

see the attached figure

we have that

The function is decreasing in the interval

$(-\infty,\text{ -3)}$

The function is increasing in the interval

$(-3,\text{ 0})\text{ U (0,}\infty)$