Question

Find the maximum or minimum value of the function.

f(x) = −
x^2/3+ 2x + 9

Answer 1

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

Answer 2

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

Answer 3

the second equation

Answer 4

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

Answer 5

algebra, well really precalc but yes algebra

Answer 6

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?

Answer 7

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?

Answer 8

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

Answer 9

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

Answer 10

The function is obviously negative, therefore concave down

Answer 11

Which means it has a maximum value

Answer 12

all you now hero..