a) 19
b) 15
c) 13
Explanation:[tex]\begin{gathered} 1)\text{ g(x) = }4x^2-5x\text{ + 1} \\ \text{average rate of change = }\frac{g(b)\text{ - g(a)}}{b\text{ - a}} \end{gathered}[/tex][tex]\begin{gathered} a)\text{ interval is 2}\le x\le4 \\ b\text{ = 4, a = 2} \\ g(4)=4(4)^2\text{ - 5(4) + 1 = 45} \\ g(2)\text{ = }4(2)^2\text{ - 5(2) + 1 = 7} \\ \text{average rate of change = }\frac{45-7}{4\text{ - 2}} \\ \text{average rate of change = 38/2} \\ \text{average rate of change = 19} \end{gathered}[/tex][tex]\begin{gathered} b)\text{ interval is 2}\le x\le3 \\ b\text{ = 3, a = 2} \\ g(3)=4(3)^2\text{ - 5(3) + 1 = 22} \\ g(2)\text{ }=4(2)^2\text{ - 5(2) + 1 }=\text{ 7} \\ \text{average rate of change = }\frac{22-7}{3-2} \\ \text{average rate of change = 15/1} \\ \text{average rate of change = 15} \end{gathered}[/tex][tex]\begin{gathered} In\text{terval is }2\le x\le2.5 \\ b\text{ = 2.5, a = 2} \\ f(2.5)=4(2.5)^2\text{ - 5(2.5) + 1 = 13.5} \\ f(2)=4(2)^2\text{ - 5(2) +1 = 7} \\ \text{average rate of change = }\frac{13.5-7}{2.5\text{ - 2}} \\ \text{average rate of change = 6.5/0.5} \\ \text{average rate of change = 13} \end{gathered}[/tex]
