Question

Cannot figure out how to set this problem up
Find the average rate of change
f(x)=x^3+1
intervals given [2,3]
book says the answer is 19, how do they get that?
no matter what I do Im not getting the correct answer.

Answer 1

\[f(x2)-f(x1)/x2-x1\]
\[f(3)-f(2)/3-2\]
\[((3)^{3}+1)-((2)^{3}+1)/1\]
\[(27+1)-(8+1)\]
\[28-9\]
\[19\]

Answer 2

we want to find the average rate of change
find f'(x)= 3x^2 (df/dx gives the change in f(x) at every instant)
now take integral between the limits 2 to 3
Average rate of change=
\[1/(3-2) \int\limits_{2}^{3} 3x^2 dx\]
\[= 1/1 * [ x^3] \]
from 3 to 2
27-8=19

Answer 3

we know that average of a function f(x) in the interval [ a,b] is given by
\[1/(b-a) \int\limits_{a}^{b} f(x) dx\]

Answer 4

Thank you both! Got it!