Posted by Hank on Sunday, June 24, 2012 at 7:16pm.
To find relative maxima and minima, first find the critical points (where f is 0 or doesnft exist).
Then examine each critical point.
It is a relative maximum if f changes from positive to negative or f is negative.
It is a relative minimum if f changes from negative to positive or f is positive.
We find the critical numbers of f by solving the equation f'( x ) = 0
f'( x ) = 3 * x ^ 2 - 2 * 3 * x
f'( x ) = 3 x ^ 2 - 6 x
f'( x ) = 3 x ( x - 2 ) = 0
So the critical numbers are x = 0 and x = 2
f ( x ) = 3 * 2 * x - 6 = 6 x - 6 = 6 ( x - 1 )
For x = 0
f = 6 * ( 0 - 1 ) = 6 * - 1 = - 6
f < 0
It is a relative maximum
For x = 2
f = 6 * ( 2 - 1 ) = 6 * 1 = 6
It is a relative minimum
Relative maximum :
x = 0
y = 0 ^ 3 - 3 * 0 ^ 2 + 4 = 4
Relative minimum :
x = 2
y = 2 ^ 2 - 3 * 2 ^ 2 + 4 = 8 - 3 * 4 + 4 = 8 - 12 + 4 = 0
If you want to see graph In google type:
functions graphs online
When you see list of results click on:
rechneronline.de/function-graphs/
When page be open in blue rectangle type:
x^3-3x^2+4
Then click option Draw
To find relative maxima and minima, first find the critical points (where f ( x ) is 0 or doesnt exist).
Then examine each critical point.
It is a relative maximum if f changes from positive to negative or f" is negative.
It is a relative minimum if f changes from negative to positive or f" is positive.
f mean f "
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