Question

Algebra problem. Confused! http://i.imgur.com/eOfJY.jpg

Answer 1

I have no idea where to begin on this one.

Answer 2

I have the solution but, I have no idea how to get there.

Answer 3

a is a constant so u need to optimise x^2(b-x)

Answer 4

So can I just plug in any number for a?

Answer 5

the solution is x=2b/3?

Answer 6

Yep

Answer 7

im trying to solve it without calculus

Answer 8

You can use calculus, it's fine.

Answer 9

Are you thinking about letting the equation equal 0?

Answer 10

just let d/dx(x^2(b-x))=0

Answer 11

Not working out for me. :/

Answer 12

we use the equation below for finding a continuous function critical points
\[\frac{d}{dx} f(x)=0\]

Answer 13

So I just simply just derive the equation?

Answer 14

I was multiplying it out first, didn't seem to work. So I had a look on Wolfram how they did it, still doesn't make sense to me. Wolfram just splits up the equation.

Answer 15

\[f(x)=x^2(b-x)=bx^2-x^3 \\ \frac{d}{dx} (bx^2-x^3)=0 \\ 2bx-3x^2=0 \\ x=0 \ or \ x=\frac{2b}{3} \\ x=\frac{2b}{3} \ \ is \ acceptable\]

Answer 16

I see. I know how I can plot this now!

Answer 17

Thanks!

Answer 18

yw