Question: Let f : [ a , b ] R b e continuous with f ( a ) = f ( b ) = 0 .

Let f:[a,b]Rbe continuous with f(a)=f(b)=0. Suppose that f''(x) exists with |f''(x)|c0>0,AAxin(a,b),
for some constant c0. Prove that
maxaxb|f(x)|c08(b-a)2x0, the derivative f'(x0)=0
Let f : [ a , b ] R b e continuous with f ( a ) =

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