Question

Найдите наименьшее значение функции y=(x^2-4x+16)/x на отрезке [1;16]

Answer 1

$y= frac{x^2-4x+16}{x} =x-4+frac{16}{x}; ,; ; ODZ:; xne 0\\y'=1-frac{16}{x^2}=frac{x^2-16}{x^2}=0; ; to ; ; x^2-16=0; ,to \\x=pm 4,; xne 0\\+++(-4)---(0)---(4)+++\\quad nearrow qquad (-4)quad searrow quad (0)quad searrow (4)quad nearrow \\x_{max}=-4; ,; x_{min}=4\\xin [, 1,16, ]\\y(1)=13\\y(4)=4\\y(16)=13\\y_{naimenshee}=y(4)=4$