The maximum value of the function y = - X3 + 48x-3 is______ ． | Math enthusiast | Mathematical art

The maximum value of the function y = - X3 + 48x-3 is______ ．

∵ y ′ = - 3x2 + 48 = - 3 (x + 4) (x-4) ∵ function y = - X3 + 48x-3 is a decreasing function in (- ∞, - 4), an increasing function in (- 4,4), and a decreasing function in (4, + ∞) ∵ function y = - X3 + 48x-3 has a maximum value of 125 when x = 4, so the answer is: 125

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