s=3t^3, have to find average velocity over interval [7,9]?

Question

i took the derivative of this equation and then subtracted teh value of f prime(7) - f prime(9). But i dont know if i am right.

Answer 1

No, that tells you beginning velocity and ending velocity and when you subtract them you get the increase of velocity over the interval.

If you want average velocity, you need distance traveled divided by total time. Plug 7 and 9 into the S formula and subtract them to get distance traveled. You don't need the derivative.

Answer 2

V = ds/dt = 9t^2
Average = [9(9)^2-9(7)^2]/(9-7)= 144

You must divide by the interval which is 9-7 = 2