Answer:
Average rate of change=22
Step-by-step explanation:
We need to find the average rate of change of the equation: [tex]y=4x^2-10x+2[/tex]between f(3) and f(5).
The formula used to find average rate of change is: [tex]Average \ rate \ of \ change=\frac{f(b)-f(a)}{b-a}[/tex]
In the given question we have a=3 and b =5
Finding f(a) i.e f(3)
[tex]f(3)=4(3)^2-10(3)+2\\f(3)=4(9)-30+2\\f(3)=36-30+2\\f(3)=8[/tex]
Finding f(b0 i.e f(5)
[tex]f(5)=4(5)^2-10(5)+2\\f(5)=4(25)-50+2\\f(5)=100-50+2\\f(5)=52[/tex]
Putting values of f(3)=8 and f(5)=52 to find average rate of change
[tex]Average \ rate \ of \ change=\frac{f(b)-f(a)}{b-a}\\Average \ rate \ of \ change=\frac{52-8}{5-3}\\Average \ rate \ of \ change=\frac{44}{2}\\Average \ rate \ of \ change=22[/tex]
So, Average rate of change=22
