The demand function for the Luminar desk lamp is given by p = f(x) = −0.1x2 − 0.3x + 32 where x is the quantity demanded in thousands and p is the unit price in dollars. (a) Find  f '(x).   (b) What is the rate of change of the unit price (in dollars per 1,000 lamps) when the quantity demanded is 4,000 units (x = 4)? $   per 1,000 lamps What is the unit price (in dollars) at that level of demand?

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