Show that x0 is a solution to the equation cosx=x^2.?

[beram700]

Let I:= [ 0,π/2 ] and let f: I --> R be defined by f(x) := sup [ x^2,cosx ] for x ϵ I. Show there exists an absolute minimum point x0 ϵ I for f on I. Show that x0 is a solution to the equation cosx=x^2.

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