Suppose a manufacturer finds that its average weekly costs of production, C (in thousands of dollars), are a function of the number of units produced, x (in hundreds).
If C(x) = 0.004 x^3-0.6 x^2+500,
then
dC/dx x=50

Question

Suppose a manufacturer finds that its average weekly costs of production, C (in thousands of dollars), are a function of the number of units produced, x (in hundreds).
If C(x) = 0.004 x^3-0.6 x^2+500,
then
dC/dx x=50

ash2326 · Answer

we have 
$$C(x)=0.004x^3-0.6x^2+500$$
take the derivative with respect to x
$$\frac{dC(x)}{dx}=0.012x^2-1.2x+0$$
let's substitute x=50
to find fdC(x)/dx at 50
$$\frac{dC(x)}{dx}_{x=50}=0.012(50)^2-1.2*50$$
$$\frac{dC(x)}{dx}_{x=50}=0.012*2500-1.2*50$$
we get
$$\frac{dC(x)}{dx}_{x=50}=-30$$

anonymous · Answer

thanks alot