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)?

you!

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

(b)Shayna is correct

(c)30 : 1

Step-by-step 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), .

Similarly for g(x),

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

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step-by-step explanation:

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