find the local maximum and local minimum for each if they exist. (INCLUDE THE VALUES)

f(x)=(1/4)x^4 - (5/3)x^3 + 3x^2

Question

find the local maximum and local minimum for each if they exist.  (INCLUDE THE VALUES)

f(x)=(1/4)x^4 - (5/3)x^3 + 3x^2

mathmale · Answer

First, I'd like to compliment you on having enclosed those fractions in parentheses.  Very appropriate, very clear.   :)

I assume this problem is one from calculus.  The first step of applying calculus to finding the local min and the local max (if either exists) is to differentiate the given function with respect to x.   

Please do that, and write your derivative here:

f '(x) = ?

amenah8 · Answer

ok, i'll do that then get back with you!

amenah8 · Answer

f prime of x = x^3 - 5x^2 +  6x

misty1212 · Answer

HI!!

misty1212 · Answer

did you get the derivative ?

misty1212 · Answer

oh yes, i see that you did
set it equal to zero and solve

misty1212 · Answer

you are lucky because this one factors

misty1212 · Answer

you good from there or no?

amenah8 · Answer

i think so. sorry, i was trying to  do it based on what you said! one moment please...

amenah8 · Answer

x^2 (x-5+6)=0   ??

anonymous · Answer

nope only x out front, not x^2

anonymous · Answer

$$x^2-5x+6)=0$$

anonymous · Answer

ok not that $$x(x^2-5x+6)=01$$

anonymous · Answer

the second part factors,so the zeros are easy to find

amenah8 · Answer

so now we are supposed to factor what is in the parenthesis?

anonymous · Answer

yes that is easier than using the quadratic formula in this case

amenah8 · Answer

but you can't factor an x out of 6? what would be the common factor?