Question

Help ASAP!! question below

Answer 1

See explanation

Explanation:

a) The y-intercept of the function f(x) is at x=0:

`f(0)=2\cdot 0^3-4\cdot 0^2+6=6`

The y-intercept of the function g(x) is
`g(0)=4.`

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
`g(3)<g(4)<g(5)<g(6).` This means g(x) is increasing too.

c) The average rate of change:

• 
  `(f(6)-f(3))/(6-3)=(2\cdot 6^3-4\cdot 6^2+6-(2\cdot 3^3-4\cdot 3^2+6))/(3)=(432-144+6-54+36-6)/(3)=90;`
• 
  `(g(6)-g(3))/(6-3)=(9-0)/(3)=3.`

Hence, the average rate of change of the function f(x) is greater than the average rate of change of the function g(x).