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Consider the following. 1( x ) = x5 + 5x2 + x - 9 Rewrite the function by dividing each term of the numerator by the denominator. Simplify the result. f(x ) = - (6x + 10) Find the derivative of the simplified function f by using the rules of differentiation. f' (x ) = 0 Demand Function for Desk Lamps The demand function for the Luminar desk lamp is given by P = f(x) = -0.1x2 - 0.2x + 22 where x is the quantity demanded in thousands and p is the unit price in dollars. (a) Find f'(x). f ' ( x ) = (b) What is the rate of change of the unit price (in dollars per 1,000 lamps) when the quantity demanded is 5,000 units (x = 5)? per 1,000 lamps What is the unit price (in dollars) at that level of demand