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which is the best estimate for the average rate of change for the quadratic function graph on the interval [tex]0 \leqslant x \leqslant 4[/tex]

Which Is The Best Estimate For The Average Rate Of Change For The Quadratic Function Graph On The Interval Tex0 Leqslant X Leqslant 4tex class=

Sagot :

The average rate of change of the given quadratic function on the interval

[tex]0\le x\le4[/tex]

is the slope of the secant line connecting the points

[tex](0,f(0))\text{ and (4,f(4)}[/tex]

In other words, the average rate of change is

[tex]m=\frac{f(4)-f(0)}{4-0}[/tex]

From the graph, we can see that f(0)=0 and f(4)=-4. By substituying these values into the last equation, we obtain

[tex]\begin{gathered} m=\frac{-4-0}{4-0} \\ m=-\frac{4}{4} \\ m=-1 \end{gathered}[/tex]

Hence the average rate of change for the given quadratic function whose graph is shown on 0≤x≤4 is -1

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