Applications of Derivatives

This chapter deals with the applications of differentiation and derivatives to solve practical problems and has five sections.The first section deals with the procedure to determine the equation of the tangent and normal to an arbitrary curve at a given point.In the second section, we turn our attention to Monotonicity or the strictly increasing / decreasing nature of functions and how the concept of derivatives can help us in determining this nature.The concept of maxima and minima is introduced in the third section and the procedure to evaluate extremum points and convexity / concavity is dealt here.Rolle’s Theorem, Lagrange’s Mean Value Theorem and Errors / Approximations is presented in the fourth section.The focus of section five is to discuss more advanced graphs by analyzing their nature using the knowledge of derivatives.At the end of this section, we have a series of exercises to test your understanding of this chapter,solved examples, previous years’ IIT JEE questions pertaining to this chapter.

In addition to preparing for the JEE mains and advanced exams, Cuemath Founder Manan Khurma's study material is helpful for students who are appearing for CBSE, ICSE and other State board exams.

Tangents and Normals

• Introduction to Tangents and Normals
• Examples on Tangents and Normals Set 1
• Examples on Tangents and Normals Set 2
• Examples on Tangents and Normals Set 3
• Examples on Tangents and Normals Set 4

Monotonicity

• Introduction To Monotonicity
• Analysing Monotonicity
• Examples on Monotonicity Set 1
• Examples on Monotonicity Set 2
• Examples on Monotonicity Set 3
• Examples on Monotonicity Set 4
• Examples on Monotonicity Set 5

Maxima and Minima

• Introduction to Maxima and Minima
• Finding Maxima and Minima Points
• Convexity and Concavity of Graphs
• Examples on Maxima and Minima Set 1
• Examples on Maxima and Minima Set 2
• Examples on Maxima and Minima Set 3
• Examples on Maxima and Minima Set 4
• Examples on Maxima and Minima Set 5

Miscellaneous Applications of Derivatives

• Rolles Theorem and Lagranges Theorem
• Examples on Rolles Theorem and Lagranges Theorem
• Errors and Approximations

Graphing Using Derivatives

• Examples on Graphing Using Derivatives Set 1
• Asymptotes In Graphs
• Examples on Graphing Using Derivatives Set 2
• Examples on Graphing Using Derivatives Set 3

Applications of Derivatives

• Solved Examples