Determine the location and value of the absolute extreme values of \( f \) on the given interval, if they exist. \( f(x)=\cos ^{2} x \) on \( [0, \pi] \) Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Type an exact answer; using \( \pi \) as needed. Use a comma to separate answers as needed.) A. The absolute maximum is \( \square \) at \( x=\square \) and the absolute minimum is \( \square \) at \( x=\square \). B. The absolute minimum is \( \square \) at \( x=\square \), but there is no absolute maximum. C. The absolute maximum is \( \square \) at \( x=\square \), but there is no absolute minimum. D. There are no absolute extreme values for \( f(x) \) on \( [0, \pi] \).
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