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# RS Aggarwal Class 12 Chapter 11 Solutions (Application of Derivatives)

RS Aggarwal Solutions for Class 12 Chapter 11 ‘Application of Derivatives’ are written to help build your aptitude to solve the exercise questions. Derivatives have wide applications in various research works as well as in daily life, and thus your syllabus contains most important theorems such as Rolle’s Theorem, Mean Value Theorem, concepts and equations of Tangents and Normals. With RS Aggarwal Solutions, You will also become well-rehearsed in finding the equations of various situations with the help of given conditions. Practising these wide-ranging questions will help you outsmart your batchmates to shine in your school, and get the college of your dreams for higher education.

A total of 8 exercises comprise 102 maths problems in all. These derivative questions cover every single topic of the CBSE syllabus in depth. Therefore, it is essential that you fill the gaps in your preparation by revising the RS Aggarwal Class 12 Solutions for Chapter 11 attentively to make the most of your study hours. It is very important that you are able to manage your time during the exam which is the arena that the Instasolv experts will intervene to aid you. The improvement in your aptitude and marks will be just the supplementary perk you will get.

The faculty of maths at Instasolv is dedicated to constantly upgrading themselves with any changes in the pattern of questions or syllabus. The answers are prepared strictly in alignment with the CBSE guidelines. You will have all your doubts sorted at just one stop and which is why Instasolv is a genuinely reliable resource to guide you through difficult questions and your homework questions.

## Important Topics Mentioned in RS Aggarwal Solutions for Class 12 Chapter 11 – Application of Derivatives

Introduction:

A derivative is a statement that gives the rate of change of a function with respect to an independent variable. It has many applications in Mathematics, Science, and Engineering.

Rate of Change of Quantities:

If a unit ‘y’ changes with a change in some other unit ‘x’ given the certainty that an equation of the form y = f(x)  is always satisfied i.e. ‘y’ is a function of ‘x’; then the rate of change of ‘y’ with respect to ‘x’ is given by

Δy/Δx =  (y2-y1) /(x2–x1)

This may sometimes be called the Average Rate of Change.

Increasing and Decreasing Functions:

Let y = f(x) be a differentiable function (whose derivative exists at all points in the domain) in an interval x = (a,b).

• If for any two points x1 and x2 in the interval x such that x1 < x2, there holds an inequality f(x1) ≤ f(x2); then the function f(x) is called increasing in this interval.
• Similarly, if for any two points x1 and x2 in the interval x such that x1 < x2, there holds an inequality f(x1) ≥ f(x2); then the function f(x) is called decreasing in this interval.

The functions are called strictly increasing or decreasing, given the inequalities are strict, i.e., f(x1) < f(x2) for strictly increasing and f(x1) > f(x2) for strictly decreasing.

Major Highlights of the Application of Derivatives:

Tangents and Normals:

Tangent: A tangent to a curve at a point on it is a line that touches the curve at that point. Also, its slope is equal to the gradient/derivative of the curve at that point.

Normal: Normal on a curve at a point on it is a line that intersects the curve and is also perpendicular to the tangent at the point. If the slope is n, and the slope of the tangent at that point is given by m; then we have m × n = -1

Approximations by Differentials:

As the name suggests, this method relies on the derivatives of the functions whose values are to be determined at some points.

• Problem – Given a function y = f(x), determine its value at x = x′.
• Approach – We will use the definition of the derivative of a function y = f(x) with respect to x.   d ( f(x) )/ dx = change in y with respect to change in x as dx → 0

Maxima and Minima:

The maxima or minima are also known as an extremum i.e. the extreme value of the function. For a function y = f(x) defined on a known domain of x. Established on the interval of x, on which the function reaches an extremum. It can be called a ‘local’ or a ‘global’ extremum.

### Exercise-Wise Discussion of Questions in RS Aggarwal Solutions for Class 12 Chapter 11 – Application of Derivatives

1. The initial exercises will help you learn various important theorems of Calculus such as the Lagrange’s mean value theorem, Rolle’s Theorem etc. through a diverse variety of questions.
2. The exercise questions in 11F and 11G are all based on maxima-minima and increasing or decreasing functions respectively.
3. In the last exercise solution 11H, you will get to polish your skills in finding the equation of a tangent and normal to different curves.
4. The questions are based on the exam pattern of CBSE as well as the entrance exam such as JEE, BITSAT and NEET.
5. You will find your scores boosted exponentially after having practised all the RD Sharma exercise questions.
6. This is also a reliable source of reference for last-minute revision right before your school exam.
7. Optimise your study timings by referring to the step by step solutions at the Instasolv Student Dashboard.

### Benefits of RS Aggarwal Solutions for Class 12 Maths Chapter 11 by Instasolv

1. The Maths faculty of Instasolv has taken up each question of RS Aggarwal Class 12 Chapter 11 exercise-wise in a detailed manner without compromising with the quality of the solutions.
2. You will also get a free of cost platform to clear all your doubts related to the Application of Derivatives.
3. We, at Instasolv, will help you understand the best possible ways to approach the maths problems of derivatives and hence we have formulated the solutions accordingly.
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