Suppose that f is continuous on [a,b], that f(x)≥0 for all x within [a,b] and that http://www.cramster.com/Answer-Board...8125008301.gif. Prove that f(x)=0 for all x within [a,b]. Also, show that the continuity hypothesis cannot be dropped.

Printable View

- December 3rd 2008, 02:58 PMbigbriemann integrable
Suppose that f is continuous on [a,b], that f(x)≥0 for all x within [a,b] and that http://www.cramster.com/Answer-Board...8125008301.gif. Prove that f(x)=0 for all x within [a,b]. Also, show that the continuity hypothesis cannot be dropped.

- December 3rd 2008, 03:24 PMPlato
Here is a hint.

If then .

Ask yourself what is the minimum value of .

Now drop continuity: . - December 4th 2008, 08:29 AMbigb