# Difference between revisions of "Calc2.52"

From Example Problems

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To find the local minimums and maximums of a function, find the critical points by finding the derivative and finding the points where it is equal to 0 or undefined. If the original function is defined at these points, then these are critical points. | To find the local minimums and maximums of a function, find the critical points by finding the derivative and finding the points where it is equal to 0 or undefined. If the original function is defined at these points, then these are critical points. | ||

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− | <math>f'(x)=\frac{1}{2\sqrt{x}}\</math> | + | <math>f'(x)=\frac{1}{2\sqrt{x}}\,</math> |

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This function is never equal to 0 as the numerator is never equal to 0. It is undefined at <math>x=0</math>. This is our only critical point. However, the square root function is only defined for nonnegative real numbers so <math>f(x)</math> is not defined to the left of <math>x=0</math>. Thus, it can not have a local minimum or maximum at <math>x=0</math>. <math>x=0</math> does give us the lowest point on the entire square root function as it starts at <math>0</math> and increases thereafter. | This function is never equal to 0 as the numerator is never equal to 0. It is undefined at <math>x=0</math>. This is our only critical point. However, the square root function is only defined for nonnegative real numbers so <math>f(x)</math> is not defined to the left of <math>x=0</math>. Thus, it can not have a local minimum or maximum at <math>x=0</math>. <math>x=0</math> does give us the lowest point on the entire square root function as it starts at <math>0</math> and increases thereafter. |

## Latest revision as of 01:53, 8 March 2006

Find the local minimums and maximums of the function .

To find the local minimums and maximums of a function, find the critical points by finding the derivative and finding the points where it is equal to 0 or undefined. If the original function is defined at these points, then these are critical points.

This function is never equal to 0 as the numerator is never equal to 0. It is undefined at . This is our only critical point. However, the square root function is only defined for nonnegative real numbers so is not defined to the left of . Thus, it can not have a local minimum or maximum at . does give us the lowest point on the entire square root function as it starts at and increases thereafter.