Solution assignment 06 Optimizing f(x)

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Assignment 6

Find the extremes of the function:


on the interval [0,2\pi]. Verify whether they are maxima or minima by using the second derivative.


The derivative of the function is:


The equation:


has the following solutions on the given interval:

x=0, x=\pi or x=2\pi

We calculate the second derivative:


For x=0 we have y''=-1 and thus there is maximum in this point.

For x=\pi we have y''=1 and thus there is minimum in this point.

Voor x=2\pi we have y''=-1 and thus there is maximum in this point.

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