Discuss the validity of each statement If the statement is always true explain why If it is not always true give a

Question

Discuss the validity of each statement If the statement is always true explain why If it is not always true give a counterexample If the area under the graph of f on a b is equal to both the left sum L and the right sum R for some positive integer n then f is constant on a b Select the correct answer below A BRE The statement is always true because if a function is either increasing or decreasing over an interval the left sum will not equal the right sum The statement is false The area under the graph of f x x 1 on 0 2 satisfies the given conditions but is OB not constant Oc The statement is always true because the only time the left sum equals the right sum is for constant functions The statement is false Any linear function on a closed and bounded interval satisfies the given conditions but is not necessarily constant D

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