Find the point of local maxima or local minima of the function
`f(x) = (sin^(4) x + cos^(4) x) " in " 0 lt x lt (pi)/(2)`

Explanation

`f(x)=sin ^{4} x+cos ^{4} x `


`=(sin ^{2} x)^{2}+(cos ^{2} x)^{2} `


`=(sin ^{2} x+cos ^{2} x)-2 sin ^{2} x cos ^{2} x `


`=1-2 sin ^{2} x cos ^{2} x `


`=1-[sin ^{2}(2 x)] / /^{2}`



We know that the range of `sin x` is `[-1,1]`, whereas the range of `sin ^{2}(2 x)` is `[0,1]`.


`0 leq sin ^{2}(2 x) leq 1`


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