Friday, May 17, 2013

Find any relative extrema of the function.

This function is defined on entire and is infinitely differentiable. The necessary condition of extremum for such a function is


The derivative of is


 


The only solution of the equation is because for all Moreover, this fact gives us that is positive for positive and negative for negative so decreases on and increases on


Therefore is the point where a local minimum is reached. The value of the function at this point is

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