Question

Relative maximum(s) & minimum(s) (extrema) of f(x)=(x-3)(x+2)^2(x+3)^2
Please Help
Fan & Medal!!

Answer 1

you got the derivative?

Answer 2

actually before we start, is this a calculus class/

Answer 3

No it's algebra 2 @satellite73

Answer 4

All i have is the equation and I have to find a series of elements of the graphed function @satellite73

Answer 5

i don't really know how to find a max and min without calc, but we can try something

Answer 6

i have graphed the equation

Answer 7

no, what i was thinking will not work.
it really says "find the extrema"?

Answer 8

with no calculus?

Answer 9

here is a nice picture of the curve
http://www.wolframalpha.com/input/?i=%28x-3%29%28x%2B2%29^2%28x%2B3%29^2+Please+Help

Answer 10

ok i think i might have a real idea this time

Answer 11

it is \[f(x)=(x-3)(x+2)^2(x+3)^2 \] the second two factors are of "multipiicity 2" meaning there is an exponent of 2 on both
that means the function does not change sign at those two factors, so a local max will be \(0\) at \(x=-2\) and at \(x=-3\)

Answer 12

as for the local minimum, good luck with that program
it looks kind of like it has a minimum at \(x=2\) but it does not

Answer 13

here is a picture on the interval \([-3.5,-.15]\) you can see the two local max
http://www.wolframalpha.com/input/?i=+%28x-3%29%28x%2B2%29^2%28x%2B3%29^2+domain+-3.5..-1.5

Answer 14

actually the interval was \([-3.5,-1.5]\)

Answer 15

i have no idea how you are supposed to find the local min, sorry

Answer 16

Actually this really helps now that I read it thank you so much! @satellite73