Question

Find the numbers b such that the average value of f(x) = 2 + 10x - 9x^2 on the interval [0,b] is equal to 3.

Answer 1

do you know how to find average value of a function?

Answer 2

Yeah. 1/(b-a) * integral of the function from a to b

Answer 3

right so we have
\[\frac{1}{b-0} \int\limits_{0}^{b} f(x) dx =3\]

Answer 4

where f=2+10x-9x^2
do you know how to find an andiderivative of f?

Answer 5

in symbols I'm asking you to compute:
\[\int\limits_{}^{}(2+10-9x^2) dx\]

Answer 6

2x + 5x^2 - 3x^3. Plug in b and multiply by 1/b

Answer 7

Would the two answers be -1/3 or 2? I did it again and got those answers

Answer 8

\[\frac{1}{b}(2b+5b^2-3b^3)=3 \]
this is what you did?

Answer 9

Yup

Answer 10

so you have
2+5b-3b^2=3

Answer 11

-3b^2+5b-1=0

Answer 12

use quadratic formula

Answer 13

Quadratic formula gives you b = -1/3 and 2, right?

Answer 14

I must've been doing something wrong over and over again

Answer 15

just checking if i have done my arithmetic right
that is the exact same quadratic you tried to find zeros for?

Answer 16

\[b=\frac{ -5 \pm \sqrt{5^2-4(-3)(-1)}}{2(-3)}\]

Answer 17

is this what you got next?

Answer 18

The online homework doesn't like those answers. But yea, that's what I did

Answer 19

\[b=\frac{-5 \pm \sqrt{25-12}}{-6}\]

Answer 20

but 13 isn't a perfect square so your answers shouldn't be so pretty

Answer 21

\[5/6 +- \sqrt{13}/6\]

Answer 22

I had written the quadratic formula wrong every time. Oops

Answer 23

lol

Answer 24

Got it. Thank you!

Answer 25

http://www.wolframalpha.com/input/?i=-3b%5E2%2B5b-1%3D0

i like using this site to check my work sometimes

Answer 26

Wolfram Alpha? I use that religiously lol

Answer 27

lol

Answer 28

so yeah the quadratic formula is
\[x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\]