Maximum value in enclosed area

Algebra Level 4

Let \(A\) be the set of points in the \(xy\)-plane such that \[ A = \left\{ (x, y) | -1 \leq x \leq 0, 0 \leq y \leq -x^{3}-x^{2}+x+1 \right\} . \] Then what is the maximum value of \( 3x + 4y ?\)

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