### Proof f(x)=x

Suppose that F is a continuous function on [0,1] and f(x) is in [0,1] for each x. Prove that f(x)=x for some x.

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Suppose that F is a continuous function on [0,1] and f(x) is in [0,1] for each x. Prove that f(x)=x for some x.

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See attached file

Please see attachment

Maximize f(x,y) = sqrt(6- x^2 - y^2) given the constraint x+y-2=0.