Question

find the maximum/minimum of the following function;

f(x) = (3x +2x^2)e^x

Answer 1

not really going to have a max is it? grows very fast

Answer 2

so your real job is to find the min, by taking the derivative, setting it equal to zero and solving for \(x\)

Answer 3

when you find the derivative, factor out the \(e^x\) and you will get a quadratic equation to solve
i think it has been cooked so the equation you get will factor and so it will be easy to find the zeros
if you get stuck let me know

Answer 4

I get stuck after i when I take the derivative and set it to zro

Answer 5

what did you get for the derivative

Answer 6

ok now factor out the \(e^x\) and combine like terms

Answer 7

e^x((4x+3)+(3x+2x^2)? is that correct?

Answer 8

yes, as step one
now combine like terms in the parentheses

Answer 9

is it clear what i mean by that?

Answer 10

(2x^2 + 7x + 3)?, I understand if this is correct :)

Answer 11

yes that is rigth

Answer 12

so derivative is \[(2x^2+7x+3)e^x\] and you want where this is equal to zero
since \(e^x>0\) always this amounts to solving \[2x^2+7x+2=0\] and this one even factors so you do not need the quadratic formula

Answer 13

you good from there?

Answer 14

yes thank you very much

Answer 15

yw

Answer 16

btw when you get your solutions, only one will be a minimum
the other will be a "local max"

Answer 17

why is that?