CUET Preparation Today
Find the maximum and minimum values of $f$, if any, of the function given by $f(x) = |x|, x \in \mathbf{R}$. |
Maximum: $0$, Minimum: None Minimum: $0$, Maximum: None Maximum: $1$, Minimum: $-1$ Minimum: $0$, Maximum: $1$ |
Minimum: $0$, Maximum: None |
The correct answer is Option (2) → Minimum: $0$, Maximum: None ##
From the graph of the given function, note that $f(x) \geq 0, \text{ for all } x \in \mathbf{R} \text{ and } f(x) = 0 \text{ if } x = 0.$ Therefore, the function $f$ has a minimum value $0$ and the point of minimum value of $f$ is $x = 0$. Also, the graph clearly shows that $f$ has no maximum value in $\mathbf{R}$ and hence no point of maximum value in $\mathbf{R}$. |
