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

$\begin{array}{1 1} Minimum=0 \\ No \;finite\;Maximum\;and\;minimum \\ Maximum =1 \\ Maximum=1\;Minimum =0 \end{array}$

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.
$f(x)=x^3+1$
As $x\to \infty f(x)\to \infty$
As $x\to -\infty f(x)\to -\infty$
Moreover $f'(x)=3x^2+1$=+ve for all $x\in R$
$f(x)$ is an increasing function through out its domain.
Hence there is no maximum and minimum values.