I'm stuck on exercise 12. I have no idea how to solve it.
Help with a proof
League 10/25/18
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I'd like some help.
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I know this is kind of a late response, but
4/x(4-x)>=1
Since it's given that 0<x<4, we know that x and 4-x are positive. So we can say
4>=x(4-x)
4>= -x² +4x
x²-4x+4>=0
(x-2)²>=0
I guess this is proof enough
Are you allowed to differentiate?
Reply to: League
Differentiating we get (8x-16)/(x*(4-x))^2. Which is zero in x=2, negative for 0 <x<2 and positive for 2<x<4. Meaning that 4/(x*(4-x)) has its lowest point on (0,4) in x=2. 4/(2*(4-2))=1. Therefore 4/(x*(4-x)) is greater than or equal to 1 on the interval (0,4).
I think this should suffice.
Reply to: Bearrito
Thanks for the help!
Reply to: League
I'm glad I could help