A twice–differentiable function f satisfies ∣f′′(x)∣≤3 for all x in [0,2]. The values f(0)=4, f(1)=3, and f(2)=1 are known. An approximation of ∫02f(x)dx is obtained by connecting the data points with straight‐line segments and finding the enclosed area.
What is the greatest possible error in this approximation?
a) 0.25
b) 1.00
c) 0.50
d) 0.125