The volume of a sphere is V = (4/3)(pi)r^3 where the radius, r is measured in micrometers (1 micrometer = 10^-6). Find the average rate of change of V with respect to r when r changes from 5 to 8 micrometers?? Am I suppose to find the derivative then solve or solve with the original function?
2007-07-11 16:46:42 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Normally when you hear "rate of change," it means you'll want to take a derivative. But when it says "AVERAGE rate of change," that's an exception. In that case, you just measure the function (in this case V(r)) at two points, and then just divide the change in the function's value (V(8)–V(5)), by the change in r (8–5).
It only turns into an actual derivative when the two points are infinitessimally close to each other.
2007-07-11 17:07:25 · answer #1 · answered by RickB 7 · 0⤊ 0⤋
Avg. rate of change = [V(8) - V(5)] / 8-5
= [682 2/3 pi - 166 2/3 pi] / 3
= 516 pi / 3
= 172 pi
No derivative needed.
2007-07-11 23:53:02 · answer #2 · answered by whitesox09 7 · 0⤊ 0⤋