Question

find the average rate of change for the following function on the indicated interval.
f(x)=3sqrt(x) ; (4, 25)

Answer 1

average is
\[\frac{1}{25}\int_4^{25} 3\sqrt{x}dx\]

Answer 2

that is a mistake

Answer 3

\[\frac{1}{21}\int_4^{25} 3\sqrt{x}dx\]

Answer 4

length of path from 4 to 25 is 21, not 25

Answer 5

might as well write
\[\frac{1}{7}\int_4^{25}\sqrt{x}dx\]
anti derivative is easy enough, it is
\[\frac{2}{3}\sqrt{x^3}\] plug in 25, 4, and subtract. ok from there or you need it worked out?

Answer 6

i think i'm good from there. i just plug 25 and 4 in for x, correct?

Answer 7

right. and don't forget the
\[\frac{1}{7}\] out front. it will be
\[\frac{1}{7}\times \frac{2}{3} (\sqrt{25}^3-(\sqrt{4})^3)\]

Answer 8

thank you so much!

Answer 9

yw

Answer 10

quick question: would i do the same thing for f(x)=x^3-2x ; (0,4)