Question

Compare the function f(x) 2x^3-4x^2+6 with function g(x) shown in the table.

(a) How does the y-intercept of f(x) compare to that of g(x)?
(b) Shayna is certain that both f(x) and g(x) are increasing on the interval (3,6) .
Is she correct? Explain your response.
(c) How does the average rate of change on the interval (3,6) of f(x) compare to that of g(x)?

THANK YOU!

Answer 1

(a) f(x) passe through (0, 4). g(x) passes through (0, 6)

(b)Shayna is correct

(c)30 : 1

Explanation:

(a)

y-axis means, for any point on y-axis, x = 0.

f(0)= 4 and g(0) = 6.

The function f(x) intercept y-axis at (0, 4) and g(x) intercepts y-axis at (0, 6).

(b)

f(3) = 24; f(4) = 70; f(5) = 156; f(6) = 294.

Hence for the function f(x),
`24 < 70 < 156 < 294`.

Similarly for g(x),
`0 < 2 < 4 < 9`

The values of the functions are increasing in the interval of (3, 6).

Hence, she is correct.

(c)

The function f(x) changes from 24 to 294. The total change (294 - 24) = 270.

For g(x), the total change in the interval (3, 6) is (9 - 0) = 9

If we compare the changes of f(x) to g(x) with the help of ratio, then it will be 270 : 9 = 30 : 1