# Find the maximum and minimum values, if any, of the following functions given by?$\;f(x)=(2x-1)^2+3$

$\begin{array}{1 1} Maximum =3 \;minimum =2 \\ Maximum =3 \;No \;finite\;minimum\;value \\ Minimum=3, No\;finite\;maximum \;value \\ Maximum=9 \;minimum =0 \end{array}$

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.
(i)$f(x)=(2x-1)^2+3$
Minimum value of $(2x-1)^2$ is Zero.
Therefore minimum value of $(2x-1)^2+3$ is 3.
There is no finite maximum value.
edited Aug 6, 2013