## Rate of change

This is one of two questions I got wrong on my exam...I would like if you could show me the right way of doing these for future use. The teacher put little notes on the assignments at the bottom. Thanks!

The Manager of a company that produces graphing calculators determines that when x thousand calculators are produced, they will all be sold when the price is p(x)=1,000/0.3x^2+8 dollars per calculator.

A. At what rate is demand p(x) changing with respect to the level of production x when 3,000(x=3) calculators are produced?

B. The revenue derived from the sale of x thousand calculators is R(x)=xp(x) thousand dollars. At what rate is revenue changing when 3,000 calculators are produced? Is revenue increasing or decreasing at this level of production?

a) dp/dx = (1000/0.3) (-2 x -3) = - 2000/(0.3x3)

When x = 3, this rate = - 2000/(0.3x3) = - 2000/(0.3*27) = - 246.9

b) R(x) = x p(x)

dR/dx = x dp/dx + p

dR/dx = x dp/dx + 1,000/0.3x^2+8

when x = 3, from part a, dp/dx = -246.9

So, at x = 3,

dR/dx = 3 * (-246.9) + 1,000/(0.3*9) + 8 = -362.3

dR/dx = -362.3 dollars/calculator

Revenue is decreasing.

**should have used quotient rule to find derivative**

I tried to post the attachment but it said invalid file.