A company’s cost function is C(x) = x2 + 2x + 4 dollars, where x is the number of units....

A company’s cost function is C(x) = x² + 2x + 4 dollars, where x is the number of units.

a. Enter the cost function in y₁ on a graphing calculator.

b. Define y₂ to be the marginal cost function by defining y₂ to be the derivative of y₁ (using NDERIV). c. Define y₃ to be the company’s average cost function,

d. Turn off the function y₁ so that it will not be graphed, but graph the marginal cost function y₂ and the average cost function y₃ on the window [0, 10] by [0, 10]. Observe that the marginal cost function pierces the average cost function at its minimum point (use TRACE to see which curve is which function).

e. To see that the final sentence of part (d) is true in general, change the coefficients in the cost function C(x), or change the cost function to a cubic or some other function [so that C(x)/x has a minimum].

Again turn off the cost function and graph the other two to see that the marginal cost function pierces the average cost function at its minimum.