Applications of Derivatives Class 12 Chapter 6 Maths is a very important chapter. The student will study the different applications of the derivatives in many fields like Science, Engineering, and many other. In this chapter students are going to learn many interesting topics like how to determine the rate of change of the quantity, finding the equations of tangents, finding turning points on the graphs for various functions and maxima and minima. Therefore the application of derivatives formulas is interesting as well as important for the students. Its strong base will definitely help a lot the students for their further course.

The main subtopics covered in this chapter are the Rate of Change of Quantities, Increasing and Decreasing Functions, Tangents and Normals, Approximations, Maxima and Minima and Maximum and Minimum values of the function for a closed interval.

In the previous chapters, students have learned exclusively on the computations of any kind of derivatives. In this chapter, the student will focus on the applications of derivatives. It is also important to always remember that such applications about computing the derivatives are essentials a lot. There are many very important applications for derivatives. Students will be looking in this chapter the use of the derivatives to determine the information about graphs of functions and optimization problems. These will not be the only applications only but scientific also. Students will also revise here limits and the derivatives which will allow us to compute the limits that they haven’t been able to compute previously. Students will also see how the derivatives can be used to estimate solutions to the equations.

In the rates of change, the student will remind themselves of the application/interpretation of derivatives in terms of rates. In the section, we will define critical points. Critical points and their concepts are very important to understand. Minimum and Maximum Values of the functions in the given interval are also important to understand. Students will see some of the basic definitions and facts involving minimum and maximum values of functions. They will determine the largest and smallest value of a function on an interval. The student will start looking at the information that the first derivatives will tell us about the graph of the function. Students will see increasing or decreasing functions as well as the First Derivative Test. In this section, the student will look at the information about the graph of the function too. We will also look at inflexion points, concavity, and the Second Derivative Test.

The student will use derivatives to compute the linear approximation to a function. They will look at the differentials as well as an application for them. They will see that derivative is like a rate measurer. Derivatives are useful to calculate the instantaneous rates of change. For example, the rate of change of position with respect to time is popular as velocity and the rate of change of velocity with respect to time is popular as acceleration. Using such ideas, the student will be able to analyse the one-dimensional particle movement given position as a function of time. Undoubtedly this chapter is for making a very essential concept about the derivatives.