Find the maximum and the minimum values, if any, of the function $f$ given by $f(x) = x^2, x \in \mathbf{R}.$
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Minimum: $0$, Maximum: None ##
From the graph of the given function, we have $f(x) = 0$ if $x = 0$. Also
$f(x) \geq 0, \text{ for all } x \in \mathbf{R}.$
Therefore, the minimum value of $f$ is $0$ and the point of minimum value of $f$ is $x = 0$. Further, it may be observed from the graph of the function that $f$ has no maximum value and hence no point of maximum value of $f$ in $\mathbf{R}$.