Difference between revisions of "Extrema"
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The ''relative'' maximum of a function is when its first derivative is zero and its second derivative is less than zero or, alternatively, its first derivative is positive approaching the point from the left and negative to its right. | The ''relative'' maximum of a function is when its first derivative is zero and its second derivative is less than zero or, alternatively, its first derivative is positive approaching the point from the left and negative to its right. | ||
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| + | To find the '''maxima''' of multi-variable functions, take the partial derivatives of the function with respect to each variable and set each of those resulting equations to zero. | ||
[[Category:mathematics]] | [[Category:mathematics]] | ||
[[Category:calculus]] | [[Category:calculus]] | ||
Revision as of 03:44, December 25, 2009
Maxima are a type of extrema or critical number for functions, which can be found with calculus.
The absolute maximum of a function on an interval is either its value at an end point or its value when its first derivative is zero and its second derivative is less than zero.
The relative maximum of a function is when its first derivative is zero and its second derivative is less than zero or, alternatively, its first derivative is positive approaching the point from the left and negative to its right.
To find the maxima of multi-variable functions, take the partial derivatives of the function with respect to each variable and set each of those resulting equations to zero.