a) Find the simplified form of the difference quotient for the function f(x) = 2x-2x+5. b) Complete the following table. h f(x+ h) - f(x) h 3 2 3 1 3 0.1 3 0.01 f(x + h) - f(x) a) The difference quotient is = h (Simplify your answer.) The graph shows the number of trips taken annually on a certain state's mass transportation system. Find the average rate of change of the number of trips from 1992 to 1995, from 1995 to 2000, and from 1992 to 1998. The average rate of change from 1992 to 1995 is million per year. (Round to three decimal places as needed.) 10- Annual Trips on a State's Mass Transportation System 9.6 million 9- 18.7 million 8.9 million 8- 7.4 million 7+ 1992 1994 1996 1998 2000 Q Utility is a type of function that occurs in economics. When a consumer receives x units of a certain product, a certain amount of pleasure, or utility U, is derived. The graph represents a typical utility function. a) Find the average rate of change of U as x changes from 0 to 1; from 1 to 2; from 2 to 3; from 3 to 4. b) Why do the average rates of change decrease as x increases? a) The average rate of change of U as x changes from 0 to 1 is (Type an integer or a decimal.) Utility (pleasure units) 150- (4,128) (3,110) 100- (2,87) (1,55) 50- - 0- 0 2 Number of units of product a) Find the simplified form of the difference quotient for the function f(x) = 3x-x. b) Complete the following table. f(x+h) - f(x) h h 4 2 4 1 4 0.1 4 0.01 a) The difference quotient is (Simplify your answer. Do not factor.)