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The maximum value of [x(x-1)+1]^(1/3),0l...

The maximum value of `[x(x-1)+1]^(1/3),0lt=xlt=1`is(A) `(1/3)^(1/3)` (B) `1/2` (C) 1 (D) 0

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To find the maximum value of the function \( f(x) = [x(x-1) + 1]^{1/3} \) for \( 0 < x < 1 \), we will follow these steps: ### Step 1: Define the function We start by defining the function: \[ f(x) = [x(x-1) + 1]^{1/3} \] ...
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