Final answer:
The marginal cost function C'(x) is obtained by differentiating the total cost function, C(x) = 175 + 1.4x. The derivative of C(x) with respect to x gives C'(x) = 1.4, which is the constant rate of change in total cost per additional unit produced.
Step-by-step explanation:
The question asks to find the marginal cost function, which represents the change in total cost when producing one more unit of output. Given the total cost function C(x) = 175 + 1.4x, the marginal cost function is found by taking the derivative of C(x) with respect to x.
Step 1: Calculate the Marginal Cost Function
To find the marginal cost function, C'(x), we differentiate C(x):
C'(x) = d/dx(175 + 1.4x) = 0 + 1.4
The derivative of a constant is 0 and the derivative of 1.4x with respect to x is 1.4. Therefore, the marginal cost function is C'(x) = 1.4.