Question

(a) Find C'(100). (What does this mean?)(b) Find the cost of producing the 101st item.(a)C'(100)dollars/item(b) Cost for the 101st item =

Answer 1

Given:

$C(x)=80+0.1x-0.003x^2+0.0005x^3$

a)

$\begin{gathered} C^{\prime}(x)=0.1-0.003(2x)+0.0005(3x^2) \\ =0.1-0.006x+0.0015x^2 \end{gathered}$$\begin{gathered} C^{\prime}(100)=0.1-0.006(100)+0.0015(100)^2 \\ =0.1-0.6+0.0015(10000) \\ =0.1-0.6+15 \\ =14.5\text{ dollars/item} \end{gathered}$