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 11 months ago
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
 11 months ago
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

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myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1Calculus or algebra?

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1Ok 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.

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

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1that 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

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

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1ok 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)

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1we have three intervals to check.

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

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

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1A 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).

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

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

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

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1dw:1393014251807:dw

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1Like 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

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

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.1good luck with your calculus
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