Answer:
See explanation
Step-by-step explanation:
a) The y-intercept of the function f(x) is at x=0:
[tex]f(0)=2\cdot 0^3-4\cdot 0^2+6=6[/tex]
The y-intercept of the function g(x) is [tex]g(0)=4.[/tex]
The y-intercept of the function f(x) is 2 units above the y-intercept of the function g(x).
b) She is correct because from the attached graph you can see that the function f(x) is increasing on the interval [3,6]. From the table, you can see that [tex]g(3)<g(4)<g(5)<g(6).[/tex] This means g(x) is increasing too.
c) The average rate of change:
- [tex]\dfrac{f(6)-f(3)}{6-3}=\dfrac{2\cdot 6^3-4\cdot 6^2+6-(2\cdot 3^3-4\cdot 3^2+6)}{3}=\dfrac{432-144+6-54+36-6}{3}=90;[/tex]
- [tex]\dfrac{g(6)-g(3)}{6-3}=\dfrac{9-0}{3}=3.[/tex]
Hence, the average rate of change of the function f(x) is greater than the average rate of change of the function g(x).
