Find the maximum and minimum value of function f(x)= 2 x+5. - Vidyadip

Question

Find the maximum and minimum value of function $f(x)=\sin 2 x+5$.

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Answer

$
\begin{array}{rlrl}
f(x) & =\sin 2 x+5 \\
\because & -1 \leq \sin 2 x \leq 1 \quad \forall x \in R \\
\therefore & -1+5 \leq \sin 2 x+5 \leq 1+5, \quad \forall x \in R \\
\Rightarrow& 4 \leq \sin 2 x+5 \leq 6 \quad \forall x \in R \\
\Rightarrow & 4 \leq f(x) \leq 6 \forall x \in R
\end{array}
$
hence maximum value is 6 and minimum value is 4 .

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