Find the average rate of change of f(x)=6x^2-3 on the interval [4,t]. Your answer will be an expression involving t.

1 answer

The average rate of change of a function f(x) on an interval [a,b] is given by (f(b) - f(a))/(b - a).

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

So, the average rate of change of f(x) on the interval [4,t] is given by:

(f(t) - f(4))/(t - 4) = (6t^2 - 3 - 6(4)^2 + 3)/(t - 4)
= (6t^2 - 3 - 96)/(t - 4)
= (6t^2 - 99)/(t - 4)

Therefore, the average rate of change of f(x) = 6x^2 - 3 on the interval [4,t] is (6t^2 - 99)/(t - 4).