if f(x)=2x^3, then the average rate of change of f on the interval [0,2] is?

Question

i dont actually want to kno the answer to this question cuz i kno how to solve it and want to solve it myself (not much of a cheater) all i need to kno is when it asks this does it want the average value of the integral or does it want the slope of the secant line of the function

Answer 1

if it ever asks for the average rate of change, it is asking for a linear function. therefore, it is the slope.

Answer 2

doesn't this question wnant you to find the slope of the line connecting the points

(0, f(0) )

and

(2, f(2) )

which looks like between
(0,0) and (2, 16)

or even forgettting about the word "slope" for a minute,

while x is changing from 0 to 2, f(x) is changing from 0 to 16

so (change in y ) /( change in x) = 16/2 = 8 ???

is that right????

Answer 3

It wants you to compute the slope (tangent to the line) over the interval.

Then it wants you compute the mean value using the mean value theorem.

Answer 4

Good question. The wording is confusing. Try this: Do it both ways and indicate which is which. Might be good for extra credit.

Answer 5

Sum(N) = Sum of ( {f(Xi+1) - f(Xi) }/N ); i=0...N, Xi = 2i/N

the limit N -> inf of {Sum(N)}//(length of Interval=2) is the average rate of change in my opinion.

and that is {f'(0) + f'(2)}/2 .... or minus ....