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

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

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

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

myininaya
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1thanks. and for the e^x...that is always positive?

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

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

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

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