(C) The table indicates both positive and negative values for f ′′(x). f ′′(x)
for a linear function would be zero for all x. Both quadratic and
exponential functions have no change in concavity for all x. A cubic
function would include a change in concavity, and f ′′(x) would be linear.
Both of these properties are indicated in the table with the given points.
Therefore, the function could be a cubic.
(A) From the integral we get a = −1, b = 3, so
Replace x with xk and
replace dx with Δx in the integrand to get the general term in the
summation.
