Find the average rate of change of f(x)=8x^2-7 on the interval [2,t]. Your answer will be an expression involving t.

Answer 1

To find the average rate of change of a function f(x) on the interval [2, t], we use the formula:

Average rate of change = [f(t) - f(2)] / (t - 2)

For the function f(x) = 8x^2 - 7, we have:

f(t) = 8t^2 - 7
f(2) = 8(2)^2 - 7 = 8(4) - 7 = 32 - 7 = 25

Therefore, the average rate of change of f(x) on the interval [2, t] is:

[(8t^2 - 7) - 25] / (t - 2) = (8t^2 - 32) / (t - 2) = 8t(t - 4) / (t - 2) = 8(t)(t - 4) / (t - 2)