Question

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?

Answer 1

Explanation:

(a) The Extreme Value Theorem.

(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.