Final answer:
The error function for Simpson's approximation measures the error of the integral approximation and involves the fourth derivative of the function being integrated. It helps determine the accuracy of the approximation based on the number of subintervals used.
Step-by-step explanation:
The error function for Simpson's approximation is a way to estimate the error made when using Simpson's Rule in numerical integration. Simpson's Rule is an approximation method for definite integrals, and it uses parabolic arcs to approximate the curve of the function being integrated.
The error function for Simpson's approximation can be calculated using the expression E = -((b-a)^5/90)*f(4)(ξ)/2880n4, where a and b are the upper and lower limits of the integral, n is the number of subintervals, and f(4)(ξ) is the fourth derivative of the function evaluated at some point ξ in the interval [a, b].
To determine if six packages of fruit snacks yield enough data for an accurate result, the associated error should be calculated, and then a judgment can be made based on the desired accuracy of the problem.