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Suppose customers in a hardware store are willing to buy N(p) boxes of nails at p dollars per box, as given by the following function. Complete parts (a) through (d) N(P) =80-3p : (25ps 5) (a) The average rate of change of f(x) with respect to x as x changes from a to b (where as b) is given by which formula? O A f(b) -f(3) f(b) - f(3) O B. b- 3 f(a + b) - f(a ) O c. lim - b . provided the limit exists lim f(a - b) + f(a) OD. b- 0 b provided the limit exists Find the average rate of change of demand for a change in price from $3 to $4. The average rate of change of demand for a change in price from 53 to $4 is (Type an integer or a decimal.) (b) The instantaneous rate of change for a function f when x = a is given by which formula? f(a - h ) O A lim , provided the limit exists ho h f(a - h) + f(a) O B. lim , provided the limit exists h Oc. lim - how ' Provided the limit exists flath ) - f (a ) OD. lim _ -, provided the limit exists 1-+ 0 h Find the instantaneous rate of change of demand when the price is $3. The instantaneous rate of change of demand when the price is $3 is (Type an integer or a decimal.) (c) Find the instantaneous rate of change of demand when the price is $4. The instantaneous rate of change of demand when the price is $4 is (Type an integer or a decimal.) (d) As the price is increased from $3 to $4, how is demand changing? Is the change to be expected? As the price increases from $3 to $4, the demand at the rate determined in part (a). This change | expected because customers are | |willing to purchase more expensive items