Changes

The ''relative'' maximum of a function is a point which at which the function takes on its largest value on some neighborhood of the point, i.e., the function takes on smaller values at all sufficiently close points.  For example, the function <math>f(x) = e^{-x^2} \cos x</math> has many relative maxima, and a unique absolute maximum at <math>x=0</math>. A relative maximum of a function can occur 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 a point which at which the function takes on its largest value on some neighborhood of the point, i.e., the function takes on smaller values at all sufficiently close points.  For example, the function <math>f(x) = e^{-x^2} \cos x</math> has many relative maxima, and a unique absolute maximum at <math>x=0</math>. A relative maximum of a function can occur 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.

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.