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If f(x)=(x^2)(e^x) then f is decreasing for all x such that A. x<-2 B. -2-2 D. x<0 E. x>0

Mathematics
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Calculus or algebra?
calculus
Ok cool stuff. So do you know how to find the derivative. The derivative is the function that tells if the original function is decreasing or increasing.

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Other answers:

i think the derivative is e^x(x^2+2x)
that is right So when is the derivative 0 (this is to find when the function is doing neither increasing or increasing) I'm asking this: solve e^x(x^2+2x)=0
e^x is never 0
So you are basically looking at solving x^2+2x=0 right now.
x=0 x=-2
ok great. Now lets check the intervals around those numbers to see if we have f'>0 (which means f is increasing) or if we have f'<0 (which means f is decreasing) So what I'm asking you to do is look at the interval (-inf,-2) Take a number from this set and see if f'>0 or <0. Then we will also check the set of numbers (-2,0) and also check (0,inf)
we have three intervals to check.
when ever you plug in a number into e^x all you need to know is that the output will always be positive
So again looking at just x^2+2x
A number from the group (-inf,-2), we could choose -4. (-4)^2+2(-4)=a positive number>0 so on this interval it is increasing. Now you check (-2,0).
for (-2,0) its negative. for (0,-inf) its positive. So the answer is B. -2
that is right
thanks. and for the e^x...that is always positive?
any positive number raised to any power will always be positve
ok. thank you.
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Like you can also look at the graph if you want it gets closer to 0 as we approach negative infinity but never touches or goes below
ohh right...i'll have to remember that graph. thanks :)
good luck with your calculus

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