Question

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

Answer 1

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!