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# Table Question

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The table of values represents a polynomial function f (x).

How much greater is the average rate of change over the interval  [5, 7]  than the interval [2, 4]?

X values:      2       3      4     5      6       7

F(x) values: 39   125  287 549 935 1469

Thanks for all of your help

Mar 30, 2018

#1
+7612
+3

avg rate of change over the interval [5, 7]   =   $$\frac{f(7)-f(5)}{7-5}$$

avg rate of change over the interval [5, 7]   =   $$\frac{1469-549}{7-5}$$

avg rate of change over the interval [5, 7]   =   $$\frac{920}{2}$$

avg rate of change over the interval [5, 7]   =   460

avg rate of change over the interval [2, 4]   =   $$\frac{f(4)-f(2)}{4-2}$$

avg rate of change over the interval [2, 4]   =   $$\frac{287-39}{4-2}$$

avg rate of change over the interval [2, 4]   =   $$\frac{248}{2}$$

avg rate of change over the interval [2, 4]   =   124

How much greater is the avg rate of change over the interval  [5, 7]  than the avg rate of change over the interval  [2, 4] ? That is...how much greater is  460  than  124 ?

460 - 124  =  336

460  is  336  greater than  124 .

Mar 30, 2018

#1
+7612
+3

avg rate of change over the interval [5, 7]   =   $$\frac{f(7)-f(5)}{7-5}$$

avg rate of change over the interval [5, 7]   =   $$\frac{1469-549}{7-5}$$

avg rate of change over the interval [5, 7]   =   $$\frac{920}{2}$$

avg rate of change over the interval [5, 7]   =   460

avg rate of change over the interval [2, 4]   =   $$\frac{f(4)-f(2)}{4-2}$$

avg rate of change over the interval [2, 4]   =   $$\frac{287-39}{4-2}$$

avg rate of change over the interval [2, 4]   =   $$\frac{248}{2}$$

avg rate of change over the interval [2, 4]   =   124

How much greater is the avg rate of change over the interval  [5, 7]  than the avg rate of change over the interval  [2, 4] ? That is...how much greater is  460  than  124 ?

460 - 124  =  336

460  is  336  greater than  124 .

hectictar Mar 30, 2018