Question: Let f:[0,1]R1 be a twice differentiable function with |f''(x)|M for all xin(0,1). Show that for all NinN,|01f(x)dx-1nk=1N12(f(kN)f(k-1N))|M3N3. It is a trapezoidal rule in calculus and

Let f:[0,1]R1 be a twice differentiable function with |f''(x)|M for all xin(0,1). Show that for all NinN,|01f(x)dx-1nk=1N12(f(kN)f(k-1N))|M3N3. It is a trapezoidal rule in calculus and may be used taylor or mean value.

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