Find the maximum and the minimum values, if any, of the function $f$ given by $f(x) = x^2, x \in \mathbb{R}$.

Maximum value: None; Minimum value: $0$

The correct answer is Option (1) → Maximum value: None; Minimum value: $0$ ##

From the graph of the given function we have $f(x) = 0$ if $x = 0$. Also,

From the graph we can see that $f(x) \geq 0$, for all $x \in \mathbb{R}$.

The minimum value is $0$ at $x = 0$.

So, there is no maximum value because if $x$ increases then value of $f(x)$ also increases.