Question

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

Answer 1

Calculus or algebra?

Answer 2

calculus

Answer 3

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.

Answer 4

i think the derivative is e^x(x^2+2x)

Answer 5

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

Answer 6

e^x is never 0

Answer 7

So you are basically looking at solving x^2+2x=0 right now.

Answer 8

x=0 x=-2

Answer 9

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)

Answer 10

we have three intervals to check.

Answer 11

when ever you plug in a number into e^x all you need to know is that the output will always be positive

Answer 12

So again looking at just x^2+2x

Answer 13

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).

Answer 14

for (-2,0) its negative.
for (0,-inf) its positive.
So the answer is B. -2<x<0 right!? :D

Answer 15

that is right

Answer 16

thanks. and for the e^x...that is always positive?

Answer 17

any positive number raised to any power will always be positve

Answer 18

ok. thank you.