‹ Back to the paper
Solve the following.
Given the total cost function for units of a commodity as: . Find: Marginal cost function Average…
Given the total cost function for $x$ units of a commodity as:
$C(x) = \frac{1}{3}x^3 + 3x^2 - 16x + 2$.
Find:
(i)[1.0]
Marginal cost function
(ii)[1.0]
Average cost function
Answer
Answer (i)
AIDifferentiating: \frac{1}{3}x^3 + 3x^2 - 16x + 2
Marginal cost $MC = \frac{dC}{dx} = \frac{d}{dx}\left(\frac13x^3 + 3x^2 - 16x + 2\right)$
Hence $MC = x^2 + 6x - 16$.
Final answer: $x^2 + 6x - 16$
Answer (ii)
AIAverage cost $AC = \frac{C(x)}{x}$
Hence $AC = \frac13x^2 + 3x - 16 + \frac2x$.
Final answer: $\frac13x^2 + 3x - 16 + \frac2x$
From ISC 2018 Mathematics Paper 1, question 19(a).