Question

Help ASAP!! question below

Answer 1

Answer:

See explanation

Step-by-step 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 $g(3)$ This means g(x) is increasing too.

c) The average rate of change:

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

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