# Math Help - Rolle's Theorem, Mean Value Theorem

1. ## Rolle's Theorem, Mean Value Theorem

2) The ordering and transportation cost C for components used in a manufacturing process is approximated by $C(x) = 10(\frac{1}{x} + \frac{x}{x+3})$, where C is measured in thousands of dollars and x is the order size in hundreds. C(3) is equal to C(6). According to Rolle's Theorem, the rate of change of the cost must be 0 for some order size in the interval (3, 6). Find that order size.

3) Determine the values a, b, c, and d so that the function f satisfies the hypotheses of the Mean Value Theorem on the interval [-1, 2].
f(x) = a if x = -1
f(x) = 2 if -1 < x <= 0
f(x) = b $x^2$ + c if 0 < x <= 1
f(x) = dx + 4 if 1 < x <= 2