9.7.11 Find the marginal cost function

Question

Find the marginal cost function.

​C(x)=210+3.3x−0.07x

C′(x) = ____________

Answer 1

The way you've written it

C(x) = 210 + 3.3x - 0.07x

which = 210 + 2.6x, combing the last two terms

C'(x) = Marginal Cost = 2.6 which means a flat horizontal MC curve, which isn't realistic, as if there were no diseconomies of scale.

BUT maybe you left out an exponent 2 on the last x term?

then C(x) = 210 +3.3x -0.07x^2 and

C'(x) = 3.3 -0.14x. this means a decreasing MC curve

trinomials tend to have descending or ascending exponents, so the last term was probably quadratic.