What is the maximum value of (x)?

If f(x) = |(1+sin^(2)x,cos^(2)x,4 sin 2x),(sin^(2)x,1+cos^(2)x,4 sin 2x),(sin^(2)x,cos^(2)x,1+4 sin 2x)| What is the maximum value of f(x)?

What is the maximum value of f(x)=3-(x-2)^(2) ?

If f(x)=" min "(4x+3, x+4)" for "x in [0, 2] , what is the maximum value of f(x) ?

If f(x)=[[1+sin^2x,cos^2x,4sin2x],[sin^2x,1+cos^2x,4sin2x],[sin^2x,cos^2x,1+4sin2x]] what is the maximum value of f(x).

f(x)=x+4 g(x)=6-x^(2) What is the maximum value of g(f(x)) ?

If y=cos x, then what is the maximum value of y?

If x+y=20 and P=xy, then what is the maximum value of P?