Suppose that f is continuous on [a,b], that f(x)≥0 for all x within [a,b] and that . Prove that f(x)=0 for all x within [a,b]. Also, show that the continuity hypothesis cannot be dropped.
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Here is a hint. If then . Ask yourself what is the minimum value of . Now drop continuity: .
Originally Posted by Plato Here is a hint. If then . Ask yourself what is the minimum value of . Now drop continuity: . Tired messing around with your hint but could not get anywehre.
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