5X12÷[-12÷{15+(4-13)}]

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zmirandalove100

19.02.2023

Mathematics

Remember that the average rate of change of a function over an interval is the slope of the straight line connecting the end points of the interval. To find those slopes, we are going to use the slope formula: $m= \frac{y_{2}-y_{1}}{x_2-x_1}$

Rate of change of

:
From the graph we can infer that the end points are (0,1) and (2,4). So lets use our slope formula to find the rate of change of

:
$m= \frac{y_{2}-y_{1}}{x_2-x_1}$
$m= \frac{4-1}{2-0}$
$m= \frac{3}{2}$
m=1.5

The average rate of change of the function

over the interval [0,2] is 1.5

Rate of change of

:
Here the end points are (0,0) and (2,2)
$m= \frac{2-0}{2-0}$
$m= \frac{2}{2}$
m=1

The average rate of change of the function

over the interval [0,2] is 1

Rate of change of

:
Here the end points are (0,-1) and (2,0)
$m= \frac{0-(-1)}{2-0}$
$m= \frac{1}{2}$
m=0.5

The average rate of change of the function

over the interval [0,2] is 0.5

Rate of change of

:
Here the end points are (0,0.5) and (2,2.5)
$m= \frac{2.5-0.5}{2-0}$
$m= \frac{2}{2}$
m=1

The average rate of change of the function

over the interval [0,2] is 1

We can conclude that the function that has the greatest rate of change over the interval [0, 2] is the function a.

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