Question

Find the x-value of all the points where the functions defined have any relative extrema. Find the value(s) of any relative extrema.

f(x) = 3xe^x + 2

Answer 1

Have you considered the 1st Derivative?

Answer 2

i don't know how to find it :/

Answer 3

I wish that made sense. Have you any other method for finding relative extrema?

Answer 4

Oh wait.. so e^x is just e^x
but I don't know what to do from there

Answer 5

Can you find f'(x), the 1st derivative?

\(f(x) = 3xe^{x} + 2\)

\(f'(x) =\;??\)

Answer 6

so 2 is a constant, so it can be ignored..

Answer 7

and I don't know what to do with the 3xe^x

Answer 8

Product Rule?

Answer 9

ohhh okay.

Answer 10

uh can you maybe walk me through that. I though I knew how to do it but I can't figure it out

Answer 11

i know its f'g + g'f

Answer 12

but I don't know what f and g are

Answer 13

Come on, these are both easy pieces.

\(f'(x) = \dfrac{d}{dx}g(x)h(x) = g(x)h'(x) + g'(x)h(x)\)

Identify g(x) and h(x).

Answer 14

is the derivative 3xe^x + 3e^x?

Answer 15

Yes. Now what?

Answer 16

so do you just use that to find out where x is undefined?

Answer 17

I though we were looking for relative extrema? \(f'(x) = 0\)

Answer 18

we are

Answer 19

Well, then find where it is zero, not where it doesn't exist.

Answer 20

so did I set this up right?
3e^x ( x + 1)

Answer 21

Yes, and that should be a very quick solution.

Answer 22

Thanks for the help I appreciate it!

Answer 23

Did you check to see that it does not also seem to be a Point of Inflection?