Question

Can someone explain this problem to me?
Find the numbers b such that the average value of
f(x) = 4 + 10x − 9x2
on the interval [0, b] is equal to 5.

Answer 1

sure

Answer 2

\[\frac{f(b)-f(0)}{b-0}=5\] is the first step

Answer 3

i didn't do anything yet really, just wrote down what the average value was
now we plug some stuff in

Answer 4

\[\frac{ 4 + 10b − 9b^2-4}{b}=5\]

Answer 5

whao what happened there?

Answer 6

@satellite73 , isnt that for avg slope ?

@Kkutie7 is this for calculus?

Answer 7

This is for calculus

Answer 8

oh is this average value as in
\[\frac{1}{b-0}\int_0^bf(x)dx=5\]?

Answer 9

guess we can do that too
thanks for the heads up @dumbcow

Answer 10

\[\frac{ 1 }{ b-a }\int\limits_{a}^{b}f(x)dx\]

Answer 11

ok I follow

Answer 12

:)

Answer 13

\[\frac{1}{b}\int_0^b (4 + 10x − 9x^2)dx=5\]

Answer 14

damn there are the question marks again
is it just me?

Answer 15

nope I'm seeing it too

Answer 16

so I set the whole thing equal to 5?

Answer 17

yeah and solve for \(b\)

Answer 18

anti derivative is \(4x+5x^2-3x^3\) plug in \(b\) plug in \(0\) (which just gives zero) divide by \(b\) ,set it equal to 5 and solve for \(b\)

Answer 19

mostly it is algebra

Answer 20

so first this right?
\[\frac{ 1 }{ b }4x + 5x^{2} −3x^{3}, x=b\]

Answer 21

i am getting those damned question marks again

Answer 22

so
\[\frac{4b+5b^{2}-3b^{3}}{b}=5\]

Answer 23

\[4+5b-3b^2=5\]
\[-3b^{2}+5b-1\]
and quadratic?

Answer 24

yeah but i would have put
\[4+5b-3b^2=5\] solve the quadratic

Answer 25

right, what you said

Answer 26

\[3b^2-5b+1=0\] etc

Answer 27

b=.2324081, 1.4342585

Answer 28

i guess

Answer 29

humm im not too sure

Answer 30

why not?

Answer 31

Well I didn't get it right and I got a hint that reads:
To find values b such that the average value of f on
[0, b]
is k, set up a function for
fave
with respect to b, and solve the equation
fave(b) = k
for b.

Answer 32

isn't that what we did?

Answer 33

I thought so. the program I'm using is saying it's wrong

Answer 34

does it want an exact answer, not a decimal?

Answer 35

probably... so Ill have to solve the quadratic by hand then

Answer 36

you could use wolfram in you like

Answer 37

Maybe mathway.com could help you? :)

Answer 38

well I can solve by hand it's just a pain.

Answer 39

\[\frac{5\pm\sqrt{13}}{6}\] no charge

Answer 40

yeah i got the same i'm gonna see if the program excepts it

Answer 41

Yes it worked! Thank you =)

Answer 42

yay!
(never doubted it)
yw