Maximum value of a product of powers

Find the maximum value of $(7 - x)^{4} (2 + x)^{5}$ when $x$ lies between $7$ and $- 2$ .

~12 minAnswer checked instantlyMaximum and minimumAM-GM inequality

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIX. Inequalities, Examples XIX.a, No. 22

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