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1 Etrema and Average Rates of Change Assignment Use the graph of each function to estimate intervals on which the function is increasing, decreasing, or constant. Support the answer numericall.. f f f Copright PreCalculusCoach.com
2 Etrema and Average Rates of Change Assignment. f if if > Approimate the relative etrema of each function Copright PreCalculusCoach.com
3 Etrema and Average Rates of Change Assignment Approimate the relative and absolute etrema of each function Estimate and classif the etrema for the graph of each function. Support the answers numericall. 9. f Copright PreCalculusCoach.com
4 Etrema and Average Rates of Change Assignment 0. f Find the average rate of change of each function on the given interval.. f + 0;. + f ; Copright PreCalculusCoach.com
5 Etrema and Average Rates of Change Assignment. f + ; 7. + f ;. f 0; Copright PreCalculusCoach.com
6 Etrema and Average Rates of Change Assignment. f + ; SOLVE THE PROBLEM 7. Maria records her distance from home over time. The values are shown in the table below. Find her average speed over the first hours. t (hours) 0 7 D t (miles) Copright PreCalculusCoach.com
7 Etrema and Average Rates of Change Assignment ANSWERS Use the graph of each function to estimate intervals on which the function is increasing, decreasing, or constant. Support the answer numericall.. f + + From the graph, it appears that: A function- + + is increasing for < A function is decreasing for > The critical point is (;. ) The table supports this conjecture f + From the graph, it appears that: A function + is increasing for < 0 and >. A function + is decreasing for 0 < <. The critical points are 0; and. ;. 8 < < < > The tables support this conjecture.. f + From the graph, it appears that: A function + is decreasing for ( ; ) The table supports this conjecture. - - Copright PreCalculusCoach.com 7
8 Etrema and Average Rates of Change Assignment. f if if > From the graph, it appears that: A function f is constant for < A function f is increasing for < < A function f is decreasing for > The critical points are ; 0 and ; < or ; < < or ; > or ; The tables support this conjecture. Approimate the relative etrema of each function Relative minimum ; Relative maimum ; Relative minimum ; Relative maimum 0. ;. Copright PreCalculusCoach.com 8
9 Etrema and Average Rates of Change Assignment Approimate the relative and absolute etrema of each function Relative minimum ; Relative maimum. ;. Absolute minimum 0; 0 No absolute maima Relative minimum. ; Relative maimum 0. ;. 9 Absolute minimum. ;. No absolute maima Estimate and classif the etrema for the graph of each function. Support the answers numericall. 9. f From the graph, it appears that: f has relative minimum in. 7 f has relative maimum in 0. 8 lim f and lim f NO O f has no absolute maima and absolute minima. <. 7 or, For interval,. 7 the function is decreasing. In. 7, f has relative minimum. For interval. 7; 0. 8 the function is increasing. In 0. 8, f has relative maimum. For interval 0. 8; the function is decreasing.. 7 < < 0. 8 or. 7; > 0. 8 or 0. 8; 0 89 The tables support this conjecture. Copright PreCalculusCoach.com 9
10 Etrema and Average Rates of Change Assignment 0. f From the graph, it appears that: f has relative maimum in 0 f has absolute minimum in. 8 and lim f and lim f NO O f has no absolute maima. <. 8 or ; < < 0 or. 8 ; For interval ;. 8 the function is decreasing. In. 8, f has absolute minimum. For interval. 8 ; 0 the function is increasing. In 0, f has relative maimum. For interval 0;. 8 the function is decreasing. In. 8, f has absolute minimum. For interval. 8 ; the function is increasing. 0 < <. 8 or 0; >. 8 or. 8 ; The tables support this conjecture. Find the average rate of change of each function on the given interval.. f + 0;. f + 0; f f f f (0 0 + ) The average rate of change on the interval 0; is. + f ; + f ; f f f f The average rate of change on the interval ; is Copright PreCalculusCoach.com 0
11 Etrema and Average Rates of Change Assignment. f + ; 7. f + ; 7 f f f 7 f ( + ) 9 ( ) The average rate of change on the interval ; 7 is. + f + f f f ; ; f f ( ) + 0 The average rate of change on the interval ; is. f 0; f f f f 0 0 ( ) Copright PreCalculusCoach.com
12 Etrema and Average Rates of Change Assignment. f + ; f f f f 0 SOLVE THE PROBLEM 7. Maria records her distance from home over time. The values are shown in the table below. Find her average speed over the first hours. t (hours) 0 7 D t (miles) Average speed over the first hours 0N0 N0 The average speed is miles per hour. 0 Copright PreCalculusCoach.com
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