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darkigloo
Group Title
If f(x)=(x^2)(e^x) then f is decreasing for all x such that
A. x<2
B. 2<x<0
C. x>2
D. x<0
E. x>0
 10 months ago
 10 months ago
darkigloo Group Title
If f(x)=(x^2)(e^x) then f is decreasing for all x such that A. x<2 B. 2<x<0 C. x>2 D. x<0 E. x>0
 10 months ago
 10 months ago

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myininaya Group TitleBest ResponseYou've already chosen the best response.1
Calculus or algebra?
 10 months ago

darkigloo Group TitleBest ResponseYou've already chosen the best response.1
calculus
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
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.
 10 months ago

darkigloo Group TitleBest ResponseYou've already chosen the best response.1
i think the derivative is e^x(x^2+2x)
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
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
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
e^x is never 0
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
So you are basically looking at solving x^2+2x=0 right now.
 10 months ago

darkigloo Group TitleBest ResponseYou've already chosen the best response.1
x=0 x=2
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
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)
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
we have three intervals to check.
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
when ever you plug in a number into e^x all you need to know is that the output will always be positive
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
So again looking at just x^2+2x
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
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).
 10 months ago

darkigloo Group TitleBest ResponseYou've already chosen the best response.1
for (2,0) its negative. for (0,inf) its positive. So the answer is B. 2<x<0 right!? :D
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
that is right
 10 months ago

darkigloo Group TitleBest ResponseYou've already chosen the best response.1
thanks. and for the e^x...that is always positive?
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
any positive number raised to any power will always be positve
 10 months ago

darkigloo Group TitleBest ResponseYou've already chosen the best response.1
ok. thank you.
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
dw:1393014251807:dw
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
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
 10 months ago

darkigloo Group TitleBest ResponseYou've already chosen the best response.1
ohh right...i'll have to remember that graph. thanks :)
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
good luck with your calculus
 10 months ago
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