can someone also help me ndertsand this question ; y=x^3 +2x^2+3 represents the rate of an object over the interval [7, 10]. What is the average rate of the object over the time interval?

Answer 1

find y at the end (x = 10)
find y at the beginning (x=3)
subtract
Yend - Ybegin

divide that by 10-7 which is 3

Answer 2

actually, the above solution applies if y is the position function. Since it is itself a rate, you need the average value of the function. That is

∫[7,10] x^3+2x^2+3 dx
----------------------------- = 782.25
     10-7