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The Class 12 RD Sharma chapter 17 exercise FBQ solution is one of the most prominent solution materials for the chapter of Maxima and Minima. RD Sharma class 12th exercise FBQ gives answers to all the necessary queries that a student might come across while solving the questions. The CBSE students have conquered differences in their performance after practicing from the RD Sharma class 12th solution of Maxima and Minima exercise FBQ.

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- Chapter 17 - Maxima and Minima - Ex 17.1
- Chapter 17 - Maxima and Minima - Ex 17.2
- Chapter 17 - Maxima and Minima - Ex 17.3
- Chapter 17 - Maxima and Minima - Ex 17.4
- Chapter 17 - Maxima and Minima - Ex 17.5
- Chapter 17 - Maxima and Minima - Ex CSBQ
- Chapter 17 - Maxima and Minima - Ex MCQ
- Chapter 17 - Maxima and Minima- Ex VSA

Maxima and Minima Exercise Fill in the blanks Question 1

Answer:Hint:

For maxima or minima we must have

Given:

Solution:

We have

Put

Now is negative (point of maxima)

So

Maxima and Minima Exercise Fill in the blanks Question 2

Answer:-1

Hint:

For maxima or minima we must have

Given:

Solution:

For maxima and minima

When

Now

Hence Minimum value of

Maxima and Minima Exercise Fill in the blanks Question 3

Answer:

Hint:

For maxima or minima we must have

Given:

Solution:

[ ]

for Maxima

Therefore

and

Maxima and Minima Exercise Fill in the blanks Question 4

Answer:Local minimum

Hint:

For maxima or minima we must have

Solution:

Let f have second derivative at c such that and ,then c is a point of local minimum.

Maxima and Minima Exercise Fill in the blanks Question 5

Answer:Local maximum

Hint:

For maxima or minima we must have

Solution:

Let c is called a point of local maxima. If there is an h > 0 such that

for all x in

The value is called the local maximum value of

Maxima and Minima Exercise Fill in the blanks Question 6

Local minimum

Hint:

For maxima or minima we must have

Solution:

Let C is called a point of local minimum. If there is an , such that

for all x in

The value is called the local minimum of

Maxima and Minima Exercise Fill in the blanks Question 7

Answer:1

Hint:

For maxima or minima we must have

Solution:

Maxima and Minima Exercise Fill in the blanks Question 8

Answer:Hint:

For maxima or minima we must have

Solution:

Let the number be , then the cube of the number is

Maxima and Minima Exercise Fill in the blanks Question 9

Answer:Hint:

For maxima or minima we must have

Given:

Solution:

Now

Thus least value of is

Maxima and Minima Exercise Fill in the blanks Question 10

Hint:

For maxima or minima we must have

Given:

Solution:

Maxima and Minima Exercise Fill in the blanks Question 12

Answer:Hint:

For maxima or minima we must have

Given:

Solution:

Let

Now differentiate it

(product rule)

For max/min

X=1

Hence maximum value of given expression occurs at x=1

Maxima and Minima Exercise Fill in the blanks Question 14

Answer:

Hint:

For maxima or minima we must have

Given:

Sum of two non-zero numbers is 4

Solution:

Let us consider

Or

That is

Or

Now

Substituting we get

Therefore

Maxima and Minima Exercise Fill in the blanks Question 15

Answer:

Hint:

For maxima or minima, we must have

Given:

x & y are two real numbers such that x >0 and

Solution:

Let where

On putting we get

but (Neglecting )

for

Hence attains minimum at

has minimum value 2.

Maxima and Minima Exercise Fill in the blanks Question 16

Answer:Hint:

For maxima or minima we must have

Solution:

Let the number be x, then

Maxima and Minima Exercise Fill in the blanks Question 17

Answer:

Hint:

For maxima or minima we must have

Given:

Solution:

is the sum of a square and a constant term. It will acquire minimum value when the square term becomes zero

Hence

is max at

Or

is local minimum

Maxima and Minima Exercise Fill in the blanks Question 18

Answer:75

Hint:

For maxima or minima we must have

Given:

Solution:

Let

Then

is minimum at x=5 and minimum value

Maxima and Minima Exercise Fill in the blanks Question 19

Answer:

Hint:

For maxima or minima we must have

Given:

Solution: we have,

To find the slope we differentiate the function once

To find the extremum points we again differentiate at equate it to zero

Now to find whether at the critical points we find a maxima or minima, we use the second derivative test

Hence we find maxima at in the equation of the slope. Hence the max value of the slope is which is

Maxima and Minima Exercise Fill in the blanks Question 20

Hint:

For maxima or minima we must have

Given:

Solution:

For extremum

for

is the point of minima

Given function has local minima at

Maxima and Minima Exercise Fill in the blanks Question 21

Answer:

Hint:

For maxima or minima we must have

Given:

Solution:

For critical points

But

as

At we will get minimum value

The least value of is

The RD Sharma chapter 12th exercise FBQ solution includes the questions from Maxima and minima, which covers the exercise FBQ consisting of only 21 questions. The FBQ section is pretty important to study as it covers the entire chapter’s concepts and includes questions from all aspects. Some of them are mentioned below:-

Maximum and minimum values of a function

First derivative test for maxima and minima

How to find Local maxima and minima

Theorem and algorithm based on higher-order derivative test

Derivatives of the function

Here are a few reasons why RD Sharma class 12 solutions chapter 17 exercise FBQ is arguably the best guide for students:-

The RD Sharma class 12th exercise FBQ is trusted by students across the country as it has been found that the questions asked in the board exams are similar to the questions provided in the textbook.

RD Sharma class 12th exercise FBQ solutions are designed by experts in maths for the better performance of students.

A student can also take help from the solutions while solving homework, as it gives a brief about the concept and saves time as well.

RD Sharma class 12th exercise FBQ solution will always have questions from the latest and updated versions of the NCERT textbooks.

You can download the RD Sharma class 12 chapter 17 exercise FBQ from the Career360 website and access all the solutions for every chapter.

The Career360 website provides online PDFs of RD sharma solutions for free of cost, so everyone can own the solutions without spending any money.

JEE Main Highest Scoring Chapters & Topics

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Download E-book- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

1. Where to download the class 12 RD Sharma chapter 17 ex FBQ solution?

Students need to navigate to the Career360 website to download the free copy of the class 12 chapter 17 solution. They can be availed for free of cost.

2. Is It okay to use RD Sharma class 12 ex FBQ for JEE mains preparation?

It is absolutely okay for students to use RD Sharma class 12 chapter 17 ex FBQ for JEE Mains preparation.

3. Does RD Sharma's class 12 exercise FBQ solution covers all the latest syllabus?

Yes, RD Sharma class 12 FBQ solution is designed to cover the latest syllabus and even receives updates to stay relevant. The latest version can be obtained from the Career360 website.

4. Can the RD Sharma class 12 exercise be used for solving homework?

Since school teachers like to give questions from NCERT books, students can use RD Sharma Solutions to find and check their homework answers.

5. How to make use of the class 12 RD Sharma chapter 17 exercise FBQ for self-practice?

Students can solve questions from their NCERT textbooks and compare answers with class 12 RD Sharma chapter 17 exercise FBQ solution to mark their performance on paper.

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