Question

Find the maximum and minimum values ,if any points at which these values occur for the following function |x+1|+2​

Answer 1

$\begin{gathered}\begin{gathered}\bf Given -  \begin{cases} &\sf{f(x) = |x + 1| + 2} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf  To \:  Find :-  \begin{cases} &\sf{maximum \: or \: minimum \: value}  \end{cases}\end{gathered}\end{gathered}$

$\large\underline\purple{\bold{Solution :- }}$

$\begin{gathered}\bf\red{We \: know,}\end{gathered}$

$\tt \:  \longrightarrow \: \purple{ |x + 1| \geqslant 0}$

$\tt \:  \longrightarrow \: \green{adding \: 2 \: on \: both \: sides}$

$\tt \:  \longrightarrow \: \pink{ |x + 1| + 2 \geqslant 2 }$

$\tt\implies \: \red{f(x) \geqslant 2}$

$\tt\implies \: \purple{f(x) \: have \: minimum \: value \: 2 \: and \: no \: maximum \: value}$