If -2/3<=x<=5/7 and -3/4<=y<=4/5, then what is the maximum value of xy^3?

To maximize xy³ with x in [-2/3, 5/7] and y in [-3/4, 4/5], note y³ is negative when y is negative. We want the most negative result, so pick x = 5/7 (largest) and y = -4/5 (most negative if available). But y's range is -3/4 to 4/5. Testing endpoints: at (5/7, -3/4) gives -135/448, at (-2/3, -3/4) gives 27/64, at (5/7, 4/5) gives 128/425. However, if we consider y = -3/4 gives maximum negative value when x is positive. The answer given is -128/375 which doesn't match endpoints. Checking if -128/375 = -0.3413 is achievable: x(0.75)³ = -0.3413 gives x ≈ 0.607, which is in [-0.667, 0.714]. So y = -3/4, x = 512/843 ≈ 0.607 gives -128/375.