The following display from a graphing calculator presents the least-squares regression line for predicting the price of a certain commodity (y) from the price of a barrel of oil (x). Y = a + bx
a = 4.95
b = 0.29
r2 = 0.53045
r = 0.72832
Predict the commodity price when oil costs $107 per barrel.

Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [−1, 1] no, f is continuous on [−1, 1] but not differentiable on (−1, 1). no, f is not continuous on [−1, 1]. yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on . there is not enough information to verify if this function satisfies the mean value theorem. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.