Question

Find all critical values of the function g(x)=5/(x²-x+6)

Answer 1

`g(x)=(5)/(x^2-x+6)\\\\D:x^2-x+6\\eq0\\\\\Delta=(-1)^2-4\cdot1\cdot6=1-24=-23 < 0\\\\x\in\mathbb{R}\\\\vertex\ of\ y=x^2-x+6\\\\p=(-(-1))/(2\cdot1)=(1)/(2)\\\\q=(-(-23))/(4\cdot1)=(23)/(4)\\\\\lim\limits_{x\to(1)/(2)}(5)/(x^2-x+6)=(5)/((23)/(4))=(5\cdot4)/(23)=(20)/(23)`


`\lim\limits_(x\to\pm\infty)(5)/(x^2-x+6)=0`