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Class 12 Mathematics-Applications of Derivatives


This seems to be , so far, the most difficult chapter in Differentiation for Class 12.  I am Suman Mathews, mathematics teacher and coach. Having a teaching experience of three decades, I can help you achieve your goals in Maths.



In my experience, most students find this topic difficult. But once they get the idea of how to go about the chapter, it becomes not so difficult after all. And that is precisely what I 'm going to tell you about here.


The chapter starts with calculating derivative as a rate measure. This part can get slightly tricky because you have to analyse each problem and then solve it. Sometimes, you may have to draw a rough sketch of the figure. There is a video and multiple choice question on this topic, towards the end of this post.


Multiple Choice question-Finding the derivative as a rate measure




There are a lot of word problems in this section. As I tell my students, read the word problem completely at first. Then tackle it sentence by sentence. 


Keep going back to the given data. I have included a multiple choice question on this topic at The next topic is calculating the equation of tangent and normaL. You'll learn how to find the equation of the tangent to the curve y = f(x) at a given point.


How to find the equation of a tangent and normal to a curve



Multiple choice question-Finding a tangent to a curve

Also learn how to calculate the equation of the normal to a curve at a given point. You'll then proceed to learn about Approximations. In this context, note that dx and dy are called the differentials of x and y respectively.


Multiple choice question on Approximations





Learn about absolute error, relative error and percentage error. The next important topic which is absolutely imperative for you to know is increasing and decreasing functions. You'll learn the conditions to determine whether a function is increasing or decreasing.


Understanding Increasing and decreasing functions



Multiple choice question-Increasing and Decreasing function

In this context, you'll make use of the method of intervals used in Quadratic Inequalities. Most problems can be solved using this method. Moving on, you'll learn about absolute maxima and minima and how to calculate them.


You'll also learn about critical points here. Last but not the least, the most important topic that you'll need to know is local maxima and minima and how to calculate it using the Second Derivative Test. There are a lot of word problems asked here .


Multiple Choice question -Finding the stationary point


Maxima Minima Word problems explained




More problems on Maxima and Minima 





How to solve Maxima and Minima word problems

Most of these require a basic knowledge of Geometry such as square, cuboid, cylinder , cone and sphere. In such problems, drawing a rough sketch helps. So, that comes to the end of all the topics that you'll need to know in Applications of Derivatives.


I can teach you all these topics together with Multiple choice questions, Assertion based questions and case study based questions. You can form a group of 5 or more students and sign up for the classes. In case you are not interested, you can access a number of free videos and multiple choice questions on this topic.


Share this page with students of Class 12 Maths who need a little extra help!


Question on Applications of Derivatives