Find values for z for which the function f grows

[AndrejN96]

Member warned about not showing an attempt.
1. Homework Statement

As the title says, I am supposed to find values for x for which the function given below grows.

f(x)=(integral from -3 to x of t^4*e^(t^2)dt)+(integral from x^2 to 2 of t*e^tdt)

Homework Equations

The Attempt at a Solution

I tried solving using substitution or partial integration but I am stuck.

 

[PeroK]

Is this what you have:

$f(x) = \int_{-3}^{x} t^4 e^{t^2} dt + \int_{x^2}^2 te^tdt$

How would you normally work out when a function is increasing?

 

[AndrejN96]

Is this what you have:

$f(x) = \int_{-3}^{x} t^4 e^{t^2} dt + \int_{x^2}^2 te^tdt$

How would you normally work out when a function is increasing?

I would find the derivative of the function and find for which values of x the value is >0. Totally overlooked it. Thank you.

 

[Delta2]

Just to say, i think you might need to put just a tiny bit more caution when calculating the derivative of $\int_{x^2}^{2}te^tdt$ wrt x.