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Find the local minimums and maximums of the function f(x)={\sqrt  {x}}.

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.

f'(x)={\frac  {1}{2{\sqrt  {x}}}}\,

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

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