Suppose f is a continuous function defined on a closed interval a,

b. (a) what theorem guarantees the existence of an absolute max- imum value and an absolute minimum value for f ? (b) what steps would you take to find those maximum and minimum values?

(b) We would differentiate the function and equate this to zero. The zeroes of the function will give us the values of the maxima / minima and we can find find the absolute maxima/minima from the results. Note we might have multiple relative maxima/ minima but only one absolute maximum and one absolute minimum.

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Suppose f is a continuous function defined on a closed interval a, b. (a) what theorem guarantees the existence of an absolute max- imum value and an absolute minimum value for f ? (b) what steps would you take to find those maximum and minimum values?

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Suppose f is a continuous function defined on a closed interval a,

b. (a) what theorem guarantees the existence of an absolute max- imum value and an absolute minimum value for f ? (b) what steps would you take to find those maximum and minimum values?