Chapter 2, Functions - Chapter 2 Test: 6

net change: $2h+h^2$ average rate of change: $2+h$

Work Step by Step

We are given: $f(t)=t^2-2t$, $t=2$ to $t=2+h$ We find the net change over the interval given: $f(2+h)-f(2)=[(2+h)^{2}-2(2+h)]-[2^{2}-2(2)]=(4+h^{2}+4h-4-2h)-(4-4)=2h+h^{2}$ We find the average rate of change over this interval: $\displaystyle \frac{f(2+h)-f(2)}{2+h-2}=\frac{2h+h^{2}}{h}=\frac{h(2+h)}{h}=2+h$

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