| Time interval | Start \({t}_{0}= 3\) | End \(t\) | \({\Delta t}\) | \(\dfrac{\Delta s}{\Delta t}=\dfrac{f(t) -f( t_{0})}{t-t_{0}}=\dfrac{16t^{2}-144}{t-3}\) |
|---|---|---|---|---|
| [3, 3.1] | 3 | 3.1 | 0.1 | \(\dfrac{\Delta s}{\Delta t} = \dfrac{f(3.1) -f(3) }{3.1-3}=\dfrac{16\cdot 3.1^{2}-144}{0.1}=97.6\) |
| [3, 3.01] | 3 | 3.01 | 0.01 | \(\dfrac{\Delta s}{\Delta t} = \dfrac{f(3.01) -f(3) }{3.01-3}=\dfrac{16\cdot 3.01^{2}-144}{0.01}=96.16\) |
| [3, 3.0001] | 3 | 3.0001 | 0.0001 | \(\dfrac{\Delta s}{\Delta t}=\dfrac{f(3.0001) -f(3)}{3.0001-3}=\dfrac{16\cdot 3.0001^{2}-144}{0.0001}=96.0016\) |