Question

On what interval(s) is the function f(x) = x^3e^(2x) increasing?
1) (-inf, -3/2], [0,inf)
2) (-inf, -3/2]
3) (-inf, 0], [3/2, inf)
4) (-inf, 3/2]
5) [-3/2, inf)

Answer 1

If f ' (x) >0 for all x in (a,b), then f is increasing
f`(x)=3x^2*e^(2x)+ x^3*2*e^(2x)=x^2e^(2x)(3+2x)
x^2e^(2x)(3+2x)>0
3+2x>0
2x>-3
x>-3/2
Function is increasing on [-3/2, inf)