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For continuous function `f: [0, 1]-> R ; A =int_0^1 (x^2* f(x))dx ; B=int_0^1 x * (f(x))^2 dx` then, maximumvalue of `A-B `is `lambda` where `[1/(4lambda)]` is

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The correct Answer is:
4
`x((x))^(2)-x^(2)f(x)=(sqrt(x)f(x))^(2)-2.sqrt(2)xxf(x).(x^(3//2))/2+(x^(3))/4-(x^(3))/4`
`(sqrt(x)f(x)-(x^(3//2))/2)^(2)-(x^(3))/4`
`:. B-A=int_(0)^(1)(sqrt(x)f(x)-(x^(3//2))/2)(2)dx=-int_(0)^(1) (x^(3))/4 dx`
`:.A-Ble 1/16`
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