# How do you find the exact relative maximum and minimum of the polynomial function of #f(x) = 2 csc x#?

The relative extremes are found where the first derivative is zero. Whether it is a maxima or minima is determined from the second derivative.

I will leave it to the student to calculate the two derivatives. The graphical representation of the derivatives in general terms is here:

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To find the exact relative maximum and minimum of the polynomial function ( f(x) = 2 \csc x ), you need to first find the critical points by finding where the derivative equals zero or is undefined. Then, you evaluate ( f(x) ) at these critical points and at the endpoints of the interval of interest. Finally, you compare the values to determine the maximum and minimum.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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