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Homework Help: Find values for z for which the function f grows

  1. Apr 9, 2015 #1
    Member warned about not showing an attempt.
    1. The problem statement, all variables and given/known data

    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)

    2. Relevant equations

    3. The attempt at a solution

    I tried solving using substitution or partial integration but I am stuck.
    Last edited by a moderator: Apr 9, 2015
  2. jcsd
  3. Apr 9, 2015 #2


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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?
  4. Apr 9, 2015 #3
    I would find the derivative of the function and find for which values of x the value is >0. Totally overlooked it. Thank you.
  5. Apr 9, 2015 #4


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