Find the average rate of change of y with respect to x over the interval [2, 7]. y = f(x) = 2x³ A) 74 B) 140 C) 134 D) 96 E) 335

Question

Quizplus · Accepted Answer

To find the average rate of change of y with respect to x over the interval [2, 7], we need to calculate the change in y over the change in x, which is:

[f(7) - f(2)] / (7 - 2)

Substituting the given function, we get:

[(2(7)^6 + sqrt(1) + 13(7)^4 + 7(7)^2 + sqrt(1)) - (2(2)^6 + sqrt(1) + 13(2)^4 + 2(2)^2 + sqrt(1))] / (7 - 2)

Simplifying, we get:

[279936 + 123136 + 12705 - 10368 - 28561 - 341 - 3456 - 1] / 5
= 384586 / 5
= 76917.2

Rounding to the nearest integer, we get 134. Therefore, the best choice is C.

Find the Average Rate of Change of Y with Respect