Question

can someone help me with this calculus problem? (attached)

Answer 1

what is \(f(1)\) ?

Answer 2

you need \(f(1)\) and \(f(5)\) then the average is
\[\frac{f(5)-f(1)}{4}\]

Answer 3

for the second part
set the derivative equal to the answer in the first part

Answer 4

you go this or no?

Answer 5

@satellite73 no i got 1.16 for f(5) and 5 for f(1). the answer choices for average value are 9/5 and 9/20

Answer 6

\[f(1)=5,f(5)=\frac{29}{25}\] so
\[f(5)-f(1)=\frac{4}{25}\] if my arithmetic is right
divide by 4 and get \(\frac{1}{25}\) is that not a choice?

Answer 7

ok i messed up

Answer 8

i get
\[f(5)-f(1)=\frac{29}{25}-5=-\frac{96}{25}\]
oh crap is this calculus average value? dang

Answer 9

yeah calc haha

Answer 10

\[\frac{1}{4}\int_1^5\frac{t^2+4}{t^2}dt\]

Answer 11

i even tried wolfram alpha and got nowhere

Answer 12

ok now lets try it
this is an easy integral

Answer 13

\[\int \frac{t^2+4}{t^2}dt=\int 1dt+\int \frac{4}{t^2}dt\] for one
then
\[\int_1^5 1dt=4\times 1=4\] and
\[\int_1^5\frac{4}{t^2}dt=\frac{16}{5}\]

Answer 14

\[4+\frac{16}{5}=\frac{36}{5}\] divide by \(4\) and get \(\frac{9}{5}\)

Answer 15

whew sorry i messed up earlier

Answer 16

i hope that is an answer choice

Answer 17

its alright, it is :) could you help me with the mean value real quick?

Answer 18

that is the mean value
i guess your next job is to solve
\[\frac{t^2+4}{t^2}=\frac{9}{5}\]

Answer 19

unless you mean another question about the mean value

Answer 20

btw is it clear how i computed the integrals?

Answer 21

no i worded it wrong. the second part of the question is to find the point where the function equals the mean value.

Answer 22

and yeah its clear now

Answer 23

ok good
is it clear how to solve that equation?

Answer 24

yeah ill try it now

Answer 25

not to hard algebra is all that is left

Answer 26

ok i got √5 and -√5 which is right. thank you so much!

Answer 27

yw
but of course \(-\sqrt5\) is not right, since it is not in the interval \((1,5)\)

Answer 28

@satellite73 wait so its only √5? and not -√5?

Answer 29

@satellite73