Find the maximum or minimum value of the function.

f(x) = −
x^2/3+ 2x + 9

Question

Find the maximum or minimum value of the function.

f(x) = −
x^2/3+ 2x + 9

anonymous · Answer

f(x)=-x^2/3+2x+9 find the max or min

anonymous · Answer

which is your question:
$\Large f(x)=-x^{\frac{2}{3}}+2x+9 $  or  $\Large f(x)=-{\frac{x^2}{3}}+2x+9 $
???

anonymous · Answer

the second equation

anonymous · Answer

ok... is this for a calculus class or algebra class?

anonymous · Answer

algebra, well really precalc but yes algebra

anonymous · Answer

ok...  
the reason i ask is because doing it the calculus way is very easy.  but since you said this is for algebra, then we'll have to complete the square to rewrite the equation in this form:
$\Large y=a(x-h)^2+k $
where (h, k) is your vertex...

do you know how to complete the square?

anonymous · Answer

nevertheless, let's start completing the square:
$\Large y=-\frac{x^2}{3}+2x+9 $
$\Large y=-\frac{1}{3}x^2+2x+9 $
$\Large y=-\frac{1}{3}(x^2-6x)+9 $

are you ok up to this point?

hero · Answer

What about just simply using x = -b/2a

anonymous · Answer

oh... yeah.... i forgot about that.... that would've been much easier...

hero · Answer

The function is obviously negative, therefore concave down

hero · Answer

Which means it has a maximum value

anonymous · Answer

all you now hero..