Average rate of change over the interval <span><span>[a,b]</span>
</span> for <span><span>y=<span>f<span>(x)</span></span></span>
</span> is given by <span><span><span><span>f<span>(b)</span></span>−<span>f<span>(a)</span></span></span><span>b−a</span></span>
</span>
Hence, average rate of change of from <span><span>x=−2</span>
</span> to <span><span>x=6</span>
</span> i.e. over the interval <span><span>[−2,6]</span>
</span> for <span><span>y=<span>f<span>(x)</span></span>=<span>12</span><span>x2</span></span>
</span> is given<span><span> rate of change=<span><span><span>f<span>(6)</span></span>−<span>f<span>(−2)</span></span></span><span>6−<span>(−2)</span></span></span></span>
</span>
As <span><span><span>f<span>(−2)</span></span>=<span>12</span><span><span>(−2)</span>2</span>=2</span>
</span> and <span><span><span>f<span>(6)</span></span>=<span>12</span><span><span>(6)</span>2</span>=</span>
</span><span>rate of change=<span><span>18−2</span>8</span>=<span>162</span>=<span>2</span></span>
Since the total number of available selections is divided by two, the probability is 50%. If we look at the total set of numbers, we find that even numbers are multiples of 2. 2, 4, 6, 8 (which makes up half of the numbers on the spinner).
