7-25 (Odd-numbered;p.224)

224 CHAPTER 2 . Functions 5-6 = Yes or No? If No, give a reason. 23. 5(1) = =: 1 = 0.1 = a+1 5. (a) Is the average rate of change of a function between 24. f( 1 ) = Vi; 1 = a, 1 = a+ h x = a and x = b the slope of the secant line through (a. f(a)) and (b. f(b)) ? 25-26 = Average Rate of Change of a Linear Function (b) Is the average rate of change of a linear function the A linear function is given. (a) Find the average rate of change of same for all intervals? the function between & = a and x = a + h. (b) Show that the 6. (a) Can the average rate of change of an increasing function average rate of change is the same as the slope of the line. ever be negative? -.25. f(x) = 1x + 3 26. 9(x) = -4x + 2 (b) If the average rate of change of a function between x = a and x = b is negative, then is the function necessarily decreasing on the interval (a, b)? SKILLS Plus 27. Average Rate of Change The graphs of the functions f and SKILLS g are shown. The function - - (f or g) has a greater aver- 7-10 = Net Change and Average Rate of Change The graph age rate of change between x = 0 and x = 1. The function of a function is given. Determine (a) the net change and (b) the - (f or g ) has a greater average rate of change between average rate of change between the indicated points on the * = 1 and x = 2. The functions f and g have the same graph. average rate of change between x = - and x = 7. 10 . 28. Average Rate of Change Graphs of the functions f, g, and h are shown below. What can you say about the average rate of change of each function on the successive intervals [0, 1 ], [1, 2], [2, 3],...? 11-24 - Net Change and Average Rate of Change A function is given. Determine (a) the net change and (b) the average rate of change between the given values of the variable. 11. f( x) = 3x - 2; x = 2, x = 3 12. r(t) = 3 - 3t; 1 = 3,1=6 13 . h (t ) = -1+ 2; 1= -4, 1 =1 14. g ( x) = 2 - 3x; x = -3, x =2 APPLICATIONS 15. h(t) = 212 - t; 1 = 3, 1 =6 29. Changing Water Levels The graph shows the depth of water W 16. f ( z ) = 1 - 322; 2 = -2, 2=0 in a reservoir over a one-year period as a function of the num- 17. f(x) = x3 - 4x2; x = 0, x = 10 ber of days x since the beginning of the year. What was the 18 . g ( t ) = 14 - 13 + 1 ; 1 = - 2 , 1 = 2 average rate of change of W between x = 100 and x = 200? * 19. f (t ) = 512; t = 3, 1 = 3 + h W ( ft ) A 100 20. f ( x ) = 1 - 3x2; x = 2, x = 2+ h 75 21. g ( x ) = =; x = 1,x = a 50 25 22. g ( x ) = -; x =0,x = h 0 100 200 300 * (days )