Maximum of a polynomial product

Find the maximum value of $x^{3} (4 a - x)^{5}$ if $x$ is positive and less than $4 a$ .

~10 minAnswer checked instantlyInequalitiesMaxima and minima

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIX. Inequalities, Examples XIX.b, No. 10 (part 1)

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).