Question

Нужно решить 5 задание

Answer 1

$y=\frac{4}{3}\cdot x^{\frac{3}{2}}-9x+22\; \; \; [\, 18,25\, ;\, 34\, ]\\\\y'=\frac{4}{3}\cdot \frac{3}{2}\cdot x^{\frac{1}{2}}-9=2\sqrt{x}-9=0\; ,\; \; \sqrt{x}=4,5\; ,\; \; x=20,25\in [\, 18,25\, ;\, 34\, ]\\\\y(20,25)=\frac{4}{3}\cdot \sqrt{20,25^3}-9\cdot 20,25+22=\\\\=\frac{4}{3}\cdot 20,25\cdot 4,5-182,25+22=-38,75\\\\y(18,25)=\frac{4}{3}\cdot \sqrt{18,25^3}-9\cdot 18,25+22=\frac{4}{3}\cdot \frac{73}{4}\cdot \frac{\sqrt{73}}{2}-164,25+22=\\\\=\frac{73\sqrt{73}}{6}-142,25\approx -38,30$

$y(34)=\frac{4}{3}\cdot 34\sqrt{34}-9\cdot 34+22=\frac{136}{3}\cdot \sqrt{34}-284\approx -19,66\\\\y_{naimenshee}=y(20,25)=-38,75$