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We need to write an example for a function $f$on an interval$[a,b]$for which the left sum and the trapezoid sum are over-approximations for every $n$.

The left sum is known to be over - approximation for a function which is decreasing monotonically in the interval $[a,b]$.The trapezoid sum is known to be over - approximation for a function which is concave upwards in the interval $[a,b]$.

Thus, to have a function whose left sum and trapezoid sum is an over - approximation create a function which is concave upwards and decreasing in the interval $\left[a,b\right]$.

The right sum is known to be over - approximation for a function which is increasing monotonically in the interval $\left[a,b\right]$.The trapezoid sum is known to be over - approximation for a function which is concave upwards in the interval $\left[a,b\right]$.

Thus, to have a function whose right sum and trapezoid sum is an over - approximation create a function which is concave upwards and increasing in the interval$\left[a,b\right]$.

The Simpson's rule approximates the area under the curve by comparing a parabolic shape for the function. Thus, the function itself is a parabolic function, the Simpson's rule would not require any approximation. Hence the error would be $0$.

Thus to have a function, which would give no error with Simpson's rule create a quadratic function.