Question

Решите плизззз :( не могу решить

Answer 1

$y = - \frac{2}{3} x { }^{ \frac{3}{2} } + 8x - 19 \\ x \geqslant 0 \\ y' = - \frac{2}{3} \times \frac{3}{2} x {}^{ \frac{3}{2} - 1} + 8 {x}^{1 - 1} = \\ = - x {}^{ \frac{1}{ 2} } + 8 = - \sqrt{x} + 8 \\ y' = 0 \\ - \sqrt{x} + 8 = 0 \\ \sqrt{x} = 8 \\ x = 8 {}^{2} \\ x = 64 \\ \\ + + + [64] - - - \\ x_{max} = 64$