Answer to Question #266650 in Calculus for toodles

Question

(1) If the total cost of a firm is c(x) = 1.5x^3 - 5x^2 + 20x + 5 . Find the marginal cost (in dollars) when 25 units are produced and sold. Where did you get the 3?

Answer 1

Given cost of firm is $C(x)=1.5 x^{3}-5 x^{2}+20 x+5$

$\begin{aligned} \text { Marginal cost }=M . C &=\frac{d C}{d x} \\ \Rightarrow M . C . &=\frac{d}{d x}\left(1.5 x^{3}-5 x^{2}+20 x+5\right) \\ &=3 \times 1.5 x^{2}-10 x+20 \\ &=4.5 x^{2}-10 x+20 \\ \text { Now M.C. } \mid x=25 &=4.5(25)^{2}-10 \times 25+20 \\ &=4.5 \times 625-250+20 \\ &=2812.5-250+20 \\ &=\ 2582.5 \end{aligned}$

About 3:

See rules of differentiation