The average rate of change on an closed interval [a,b] is given by
So in your case . And the average rate of change is given by
For the second part, just use the mean value theorem
I need some help with this problem:
A company introduces a new product for which the number of units sold S is given by the equation below, where t is the time in months.
I need to:
a) Find the average rate of change of S(t) during the first year (rounded to 1 decimal place).
And:
b) During what month does S'(t) equal the average rate of change during the first year?
I'm not too sure what to do for the first one. Some people have told me to find the derivative of the problem then plug 12 in for t, but that's not right. I could probably find B after I find A.
Bump...
Ok, so I got 182.8125 for S(12) and 56.25 for S(0). Subtracting the two and dividing by 12 gives me 10.6 (rounding to one decimal).
So I took the derivative of the original problem and set it equal to 10.6. I got two answers; -11.9799 and 3.97993.
This is the last submission I have for this problem, so I need to make sure this is right ahead of time. Is part A correct? For part B, I just have to choose the month from a drop-down menu.
I figured out part A, that was sorta simple (after seeing what others have posted). I guess I got the answer wrong, because I put 10.6 (rounding up...), but I guess they were looking for 10.5.
So anyway, I sort of understood part B. Although the correct month was May, I didn't understand how they got that.