Let f belong to C[a,b] be a function whose derivative exits on (a,b).

Suppose f is to be evaluated at d in (a,b), but instead of computing the actual value f(d), the approximate value,f~(d), is the actual value of f at (d+epsilon), that is f~(d)=f(d+epsilon)

Use the mean value theorem to estimate the absolute error:f(d)-f~(d)and the relative error: (f(d) - f~(d)) / f(d)