Question

Johnny's Tumblers sells plastic cups in bulk for start-up restaurants. Their cost for producing these is modeled by: c(x) = 0.02x^2 + 0.5x + 40

a) Since the marginal cost is found by taking the derivative, the formula for c'(x)= ? (My answer: 0.04x + 0.5)

b) The marginal average cost would be the derivative of the average cost function. Find this marginal average cost function. The symbolic notation for this is: c'(x) (with a line over the c) = ?????
This is the part I need help with.

Answer 1

a. correct
b. average cost function= costtotal/x= .02x+.05+40/x

marginal average cost=d/dx C(x)
= .02-40/x^2

Answer 2

a) ok
b) The average cost is the cost per unit, or c̅(x) = c(x)/x

So, c̅(x) = 0.02x + 0.5 + 40/x

The marginal average cost is thus

c̅'(x) = 0.02 - 40/x^2