Question

Find the average rate of change of the function f(x)=2x^3-x from [4,6].

PLEASE HELP!

Answer 1

151

Explanation:

Average Rate of Change Formula

`(f(b)-f(a))/(b-a)\\(f(6)-f(4))/(6-4) \\(((2*6^3)-6)-((2*4^3)-4))/(2) \\((432-6)-(128-4))/(2) \\(426-124)/(2)\\\\ (302)/(2) = 151`

If you have trouble remembering the rate of change formula, it's the same as the slope formula.

`f(b) = y_2\\f(a) = y_1\\b = x_2\\b = x_1\\slope = (y_2-y_1)/(x_2-x_1) \\`

Similarly to the slope formula, it doesn't matter which point you set up to be the second coordinate, as long as it is consistent across the numerator and denominator.

Answer 2

The average rate of change of a function f(x) over the interval [a, b] is given by the formula:

average rate of change = (f(b) - f(a)) / (b - a)

In this case, the function is f(x) = 2x^3 - x and the interval is [4, 6]. So we have:

f(4) = 2(4)^3 - 4 = 124

f(6) = 2(6)^3 - 6 = 330

Therefore, the average rate of change of f(x) over [4, 6] is:

(330 - 124) / (6 - 4) = 103

So the average rate of change of the function f(x) over the interval [4, 6] is 103.