Find the maximum and minimum values of $f,$ if any,of the function given by $f(x)=|x|, x \in R.$
(N/A) From the graph of the given function,note that:
$f(x) \geq 0$ for all $x \in R$ and $f(x)=0$ if $x=0.$
Therefore,the function $f$ has a minimum value of $0$ and the point of minimum value of $f$ is $x=0.$
Also,the graph clearly shows that $f$ has no maximum value in $R$ and hence no point of maximum value in $R.$
$f(x) \geq 0$ for all $x \in R$ and $f(x)=0$ if $x=0.$
Therefore,the function $f$ has a minimum value of $0$ and the point of minimum value of $f$ is $x=0.$
Also,the graph clearly shows that $f$ has no maximum value in $R$ and hence no point of maximum value in $R.$
Explore More
Similar Questions
If $y = a \log x + b x^2 + x$ has its extreme values at $x = -1$ and $x = 2$,then the value of $\left(\frac{a}{b} + \frac{b}{a}\right)$ is
If $(2, a)$ and $(b, 19)$ are two stationary points of the curve $y=2x^3-15x^2+36x+c$,then $a+b+c=$
If the petrol burnt in driving a motor boat varies as the cube of the velocity,then the speed (in $km/h$) of the boat relative to the water,going against a water flow of $C \ km/h$,so that the quantity of petrol burnt is minimum,is:
If $m$ and $n$ respectively are the number of local maximum and local minimum points of the function $f(x) = \int_{0}^{x^{2}} \frac{t^{2}-5t+4}{2+e^{t}} dt$,then the ordered pair $(m, n)$ is equal to
DifficultJEE MAIN 2022
View Solution$A$ poster is to be printed on a rectangular sheet of paper of area $18 \ m^2$. The margins at the top and bottom of $75 \ cm$ each and at the sides $50 \ cm$ each are to be left. Then the dimensions,i.e.,height and breadth of the sheet,so that the space available for printing is maximum,are respectively:
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo