Sunday, April 14, 2013

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


To find the derivative of this function we need the product rule and the derivatives of sine, cosine, hyperbolic sine and hyperbolic cosine. We know them:)


So  


The function is always positive, hence at those points where They are for integer and three of them are in the given interval: and


Moreover, has the same sign as so it is positive from to negative from to positive from to and negative again from to Function increases and decreases accordingly, therefore it has local minima at and and local maxima at and

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Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

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