Find values for z for which the function f grows

AndrejN96
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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.
 
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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?
 
PeroK said:
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.
 
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.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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