Posted by Subhotosh Khan on August 12, 2002 at 14:04:13:
In Reply to: max & min posted by scott rein on August 12, 2002 at 13:30:59:
: I need help understanding maximums and minimums here is a example problem x^3-6x^2+12x-4 I need to know how to get the set points and whether it is a max or min
***********************************
In short
Set dy/dx = 0 to find maxima and minima
at relative maxima = d^2y/dx^2 < 0
at relative minima = d^2y/dx^2 > 0
So
y = x^3 - 6x^2 +12x -4
y' = 3x^2 - 12x + 12
set y' = 0
0 = 3x^2 - 12x + 12
0 = 3(x-2)^2
so at x = 2 you have a relative maximum/minimum
test:
y" = 6x -12
at x = 2, y" = 0
So at x = 2, the function has a point-of-inflection ( a change of curvature - neither maximum nor minimum).