Question

how do i find average rate of the fucntion over the gviing time.
f(t)= 2t+7 [1,2]

Answer 1

Let f be a function which is continuous on the closed interval [a, b]. The average value of f from x = a to x = b is the integral

\[(1\div(b-a))\int\limits_{a}^{b}f(x)dx\]

Answer 2

so evaluating the integral value we get the result as 10

Answer 3

That's the average area underneath the function, however the average rate is the derivative. How fast is your function changing?

Since the original function is linear, its rate of change is constant at 2.