RS Aggarwal Class 12 Solutions Chapter-11 Applications of Derivatives

Application of Derivatives

The application of derivatives is used for the determination of various things like Rolle’s Theorem, Lagrange’s Mean Value Theorem, derivatives, finding the rate of change, intervals decreasing or increasing, display increase or decrease in whole domain, finding the slope of the tangent, the approximate value of numbers and many other things. It will explain derivatives from composite function, inverse trigonometric function, implicit function, and exponential function. All these are explained in engineering and social sciences. Other concepts discussed here are:

• Equation of tangent. 

• Maximum and minimum values of the function.

• Interval increases and decreases.

• Approximation and errors. 

Advantages of using RS Aggarwal Class 12 Application of Derivatives Solutions to prepare for the Exams

RS Aggarwal Application of Derivatives Solutions provides a good resource and study material for exam preparation. All the questions and solutions designed in this textbook are in accordance with the CBSE exam pattern and syllabus. Students can take leverage from this RS Aggarwal book to understand the practical questions that come in the examination. One can also take help from this book in solving their daily homework, practice set, answering model questions, and others. Some of the advantages are explained to the students.

• Easy to access and ready-made solutions for every chapter. 

• Simple and student-friendly explanations to help them in solving the problems quickly. 

• It incorporates all the chapters included in the Class 12 Maths books for CBSE. 

• Chapter-wise solutions are provided in detail for easy comprehension. 

• All the solutions are based on the last ten years of question patterns by the subject experts. 

Exercise Questions in RS Aggarwal Class 12 Solutions Application of Derivatives

Question 1

Sol: The side of a square is c.

The rate of change of a side = dc/dt = 0.4 cm/s

Therefore, the perimeter of the square = 4c

The rate of change in the perimeter of the square= dc/dt = 4x 0.4

So, dc/dt = 1.6 cm/s

Question 2

Sol: The radius of a circle= m. 

The circumference of the circle = 2πr

Given, the rate of change of a side = dm/dt = 0.76 cm/s

Therefore, the rate of change of circumference of the circle = 2πr dm/dt

The rate of change in the perimeter of the square= 2 x 1.3 x 0.76

So, dm/dt = 1.976 cm/s

Question 3

Sol: A globe is in the shape of a sphere

Let’s assume the radius of the globe is represented with s

The surface area of the globe sphere = 4πr²

ds/dt = 0.43 cm/s

Therefore, the rate of change of the surface area of the globe sphere = 8πr² ds/dt

= 8 x 1.7 x 7 x 0.43

ds/dt = 40.936 cm²/s

Question 4

The radius of a circle is expanding evenly at the rate of 0.2 cm/s. State at which rate is the area increasing when the radius is 20 cm? (Take π = 3.14.)

Sol: Consider the radius of the circle as c

dc/dt = 0.2 cm/s

We are already familiar, that area of the circle = πr2

Here the rate of change of area = 2πr ds/dt

By putting the values

= 2 × 3.14 × 20 × 0.2

dc/dt = 25.12 cm²/s

The RS Aggarwal Class 12 Solutions Application of Derivatives is also helpful for students making advance preparation in higher studies. The concept discussed here is really helpful for various examinations like JEE, NEET, BITSAT, etc.