Найдите наибольшее и наименьшее значение значение функции y=3√2X^2(X-5)на промежутке [2;-8]
Под корнем только 2?
нет все выражение
![y=3 \sqrt{2x^2(x-5)} , \ [5;8]\\
x-5 \geq 0\\
x \geq 5\\
y'= \frac{3}{2 \sqrt{2x^2(x-5)} } (2x^3-10x^2)'= \frac{3(6x^2-20x)}{2 \sqrt{2x^2(x-5)}}= \frac{3(3x^2-10x)}{ \sqrt{2x^2(x-5)} }\\
y'=0\\
3x^2-10x=0\\
x(3x-10)=0\\
x_1=0\ \textless \ 5\\
3x-10=0\\
x_2= \frac{10}{3}\ \textless \ 5](https://tex.z-dn.net/?f=y%3D3+%5Csqrt%7B2x%5E2%28x-5%29%7D+%2C+%5C+%5B5%3B8%5D%5C%5C%0Ax-5+%5Cgeq+0%5C%5C%0Ax+%5Cgeq+5%5C%5C%0Ay%27%3D+%5Cfrac%7B3%7D%7B2+%5Csqrt%7B2x%5E2%28x-5%29%7D+%7D+%282x%5E3-10x%5E2%29%27%3D+%5Cfrac%7B3%286x%5E2-20x%29%7D%7B2+%5Csqrt%7B2x%5E2%28x-5%29%7D%7D%3D+%5Cfrac%7B3%283x%5E2-10x%29%7D%7B+%5Csqrt%7B2x%5E2%28x-5%29%7D+%7D%5C%5C%0Ay%27%3D0%5C%5C%0A3x%5E2-10x%3D0%5C%5C%0Ax%283x-10%29%3D0%5C%5C%0Ax_1%3D0%5C+%5Ctextless+%5C+5%5C%5C%0A3x-10%3D0%5C%5C%0Ax_2%3D+%5Cfrac%7B10%7D%7B3%7D%5C+%5Ctextless+%5C+5+%0A "y=3 \sqrt{2x^2(x-5)} , \ [5;8]\\
x-5 \geq 0\\
x \geq 5\\
y'= \frac{3}{2 \sqrt{2x^2(x-5)} } (2x^3-10x^2)'= \frac{3(6x^2-20x)}{2 \sqrt{2x^2(x-5)}}= \frac{3(3x^2-10x)}{ \sqrt{2x^2(x-5)} }\\
y'=0\\
3x^2-10x=0\\
x(3x-10)=0\\
x_1=0\ \textless \ 5\\
3x-10=0\\
x_2= \frac{10}{3}\ \textless \ 5")