UPTAC B.Tech Merit List 2025 - Check Dates, Tie-Breaking Procedure

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.

  • 91 Questions around this concept.

Solve by difficulty

Let $f(x)=x^3-x^2+x$ then number of points which are either local maxima or local minima is ?

If m and M are the minimum and the maximum values of

4+\frac{1}{2}\sin ^{2}2x-2\cos ^{4}x\, ,x\, \epsilon \, R,

 then Mm 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 :

 If x= -1 and x = 2 are extreme points of  f\left ( x \right )= \alpha \log \left | x \right |+\beta x^{2} +x then 

Let a,b,\epsilon R  be such that the function f given by f(x)=ln \left | x \right |+bx^{2}+ax,x\neq 0

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= \frac{1}{2} \: and\: b=\frac{-1}{4}.

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 :

GNA University B.Tech Admissions 2025

100% Placement Assistance | Avail Merit Scholarships | Highest CTC 43 LPA

UPES B.Tech Admissions 2025

Ranked #42 among Engineering colleges in India by NIRF | Highest Package 1.3 CR , 100% Placements | Last Date to Apply: 15th July

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

Best Public Engineering Institutes 2025
Discover the top public engineering colleges in India beyond IITs and NITs for 2025. Get insights on placements, eligibility, application process, and more in this comprehensive ebook.
Check Now

$\mathrm{f\left ( x \right )= x^{3}-3x+4}$ has local minimum at

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

Maxima and Minima of a Function

"Stay in the loop. Receive exam news, study resources, and expert advice!"

Get Answer to all your questions

Back to top