EASYAmity University Noida-B.Tech Admissions 2026
Among top 100 Universities Globally in the Times Higher Education (THE) Interdisciplinary Science Rankings 2026
Search Colleges, Exams, Schools & more
Login
Maxima and Minima in Calculus - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
-
Maxima and Minima of a Function is considered one the most difficult concept.
-
85 Questions around this concept.
Solve by difficulty
If m and M are the minimum and the maximum values of
then M−m is equal to :
The maximum volume (in cu.m) of the right circular cone having a slant height of 3 m is:
Let the tangents drawn to the circle, $x^2+y^2=16$ from the point $P(0, h)$ meet the $x$ axis at points A and B. If the area of $\triangle A P B$ is minimum, then n is equal to :
JEE Main 2026 Session 2: Result Link | Final Answer Key
JEE Main 2026: College Predictor | Official Question Papers
Comprehensive Guide: IIT's | NIT's | IIIT's | Foreign Universities in India
Don't Miss: India's Best B.Tech Counsellors in your city - Book Your Seat
If x= -1 and x = 2 are extreme points of then
Let be such that the function f given by
has extreme values at x = –1 and x = 2.
Statement 1: f has a local maximum at x = –1 and at x = 2.
Statement 2 : .
A wire of length 2 units is cut into two parts which are bent respectively to form a square of side=x units and a circle of radius=r units. If the sum of the areas of the square and the circle so formed is minimum, then :
Which of the following graphs represents local maximaa at x = a
The function $f(x)=2 x+3(x)^{\frac{2}{3}}, x \in \mathbb{R}$, has
$\mathrm{f\left ( x \right )= x^{3}-3x+4}$ has local minimum at
JEE Main 2026 College Predictor
Check your college admission chances based on your JEE Main percentile with the JEE Main 2026 College Predictor.
Try NowWhich is the correct for the following figure
Concepts Covered - 1
Maxima and Minima of a Function
Maxima and Minima of a Function
Let $y=f(x)$ be a real function defined at $x=a$. Then the function $f(x)$ is said to have a maximum value at $x=a$ if $f(x) \leq f(a) \quad \forall a \in R$.
And also the function $f(x)$ is said to have a minimum value at $x=a$, if $f(x) \geq f(a) \quad \forall a \in R$
Concept of Local Maxima and Local Minima
The function $f(x)$ is said to have local maxima (or maxima) at a point 'a' if the value of $f(x)$ at ' $a$ ' is greater than its values for all $x$ in a small neighbourhood of ' $a$ '. In other words, $f(x)$ has a maxima at $x=$ ' $a$ ', if $f(a+h) \leq f(a)$ and $f(a-h) \leq f(a)$, where $h>0$ (very small quantity).
The function $f(x)$ is said to have local minima (or minima) at a point 'b' if the value of $f(x)$ at 'b' is less than its values for all $x$ in a small neighbourhood of 'b'. In other words, $f(x)$ has a maximum at $x=$ 'b', if $f(b+h) \geq f(b)$ and $f(b-h) \geq f(b)$, where $h>0$ (very small quantity).
Study it with Videos
"Stay in the loop. Receive exam news, study resources, and expert advice!"