If f(x)= -x^(3)+6x^(2)-9x-2, how do you find the relative minim value?
but really...i'm stuck here..how do you solve this equal to 0?
-3x^(2)+12x-9=0?
2007-12-15 09:59:17 · 2 answers · asked by remote control 1 in Science & Mathematics ➔ Mathematics
-3x² + 12x - 9 = 0
Try to think back to your algebra classes. Remember when your teacher taught you how to solve quadratic equations? Yeah, this is one of those.
-3x² + 12x - 9 = 0
x² - 4x + 3 = 0
(x - 3)(x - 1) = 0
x=3 ∨ x=1
Now all you need to do is find out which one's the minimum. This is easiest done by finding the second derivative at each point. The second derivative is f''(x) = -6x + 12, f''(1) = 6, f''(3) = -6, so 1 is the local minimum and 3 is the local maximum (there are several other ways to determine that, including simple examination of the geometry of the cubic).
2007-12-15 10:21:17 · answer #1 · answered by Pascal 7 · 0⤊ 0⤋
Yes, you're right about the second equation, obtained by setting
f '(x) = 0
It has two solutions.
2007-12-15 18:04:10 · answer #2 · answered by nicholasm40 3 · 0⤊ 0⤋