Question

State the maximum and mini mum value of f(x)= x^2+9

Answer 1

$f(x)= x^2+9\\\\for\ each\ x\in R\\\\x^2 \geq 0\ \ \ \Rightarrow\ \ \ x^2+9 \geq 9\ \ \ \Rightarrow\ \ \ f(x) \geq 9\\\\y_{min}=9\\ y_{max}\ \ \ \rightarrow\ \ \ not\ exist$

Answer 2

$a>0 \Rightarrow \hbox{no maximum}$

$y_{min}=\frac{-b^2+4ac}{4a}\\y_{min}=\frac{-0^2+4\cdot1\cdot9}{4\cdot1}\\ y_{min}=9$