Function f(x)=(x^3)(e^x) is strictly increasing on the interval of?

1 Answer
Jun 24, 2018

Find the first derivative:

#f’(x) = 3x^2e^x +x^3e^x#

Now determine the values of #x# for which #f’(x) = 0#.

#3x^2e^x + x^3e^x =0#

#x^2e^x(3+ x) = 0#

It follows that #x = 0# and x=-3#

We see that the derivative is positive whenever #x> -3#, thus #f(x)# is strictly increasing on #(-3, oo)#.

Hopefully this helps!