Browse Questions

# Find the maximum and minimum values, if any, of the following functions given by $(iv) \: f (x) =\mid\sin 4x+3\mid$

This is fourth part of multipart q2

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.
$f(x)=\mid\sin 4x+3\mid$
Let $f(x)=\mid \sin 4x+3\mid$
Maximum value of $\sin 4x$ is 1
$\therefore$ maximum value of $\mid\sin 4x+3\mid=\mid 1+3\mid=4$
Minimum value of $\sin 4x$ is $-1$
$\therefore$ Minimum value of $\mid\sin 4x+3\mid=\mid -1+3\mid=2$