# Find the maximum and minimum values, if any, of the following functions given by?$f(x)=9x^2+12x+2$

$\begin{array}{1 1} Maximum =10 \\ \text{No finite maximum} \\ Minimum =4 \\ Maximum =2 \end{array}$

Toolbox:
• $f$ is said to have a maximum value in $I$ , if there exist a point c in I such that $f(c) \geq f (x)$ for all $x \in I$.The number $f( c)$ is called the maximum value of f in I and the point c is called a point of maximum value of f in I
• $f$ is said to have a minimum value in $I$ , if there exist a point $c$ in I such that $f(c) \leq f (x)$ for all $x \in I$.The number $f(c)$ is called the minimum value of f in I and the point $c$ in this case is called a point of minimum value of $f$ in I
• $f$ is said to have a extreme value in $I$ , if there exist a point $c$ in I such that f(c) is either a maximum value or minimum value of $f$ in $I$. The number $f (c)$ in this case is called the extreme value of $f$ in $I$ and the point $c$ is called the extreme point.
$f(x)=9x^2+12x+2$
$\qquad\;\;=(3x+2)^2-2$
Minimum value of $(3x-2)^2$ is zero.
Minimum value of $(3x+2)^2-2=9x^2+12x+2$ is -2
$f(x)$ does not have finite maximum value.