JEE Exam > JEE Notes > Mathematics (Maths) Main & Advanced > Flashcards: Application of Derivatives
Flashcards: Application of Derivatives
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1 APPLICATION OF DERIVATIVES The notion of derivatives was introduced to solve problems of physics concerning motion of an object. The velocity of an object is a measure of the rate of change of distance with respect to time. Acceleration is a measure of the rate of change of velocity with respect to time. This rate of change is precisely given by the notion of derivative. The derivative is also used to find the equation of tangent to a curve at a specific point. Page 2 APPLICATION OF DERIVATIVES The notion of derivatives was introduced to solve problems of physics concerning motion of an object. The velocity of an object is a measure of the rate of change of distance with respect to time. Acceleration is a measure of the rate of change of velocity with respect to time. This rate of change is precisely given by the notion of derivative. The derivative is also used to find the equation of tangent to a curve at a specific point. TANGENT AND NORMAL Let ?? =?? (?? ) be the equation of a curve. At a point ?? , on the curve, the value of ???? ???? (if defined) gives the slope the tangent (=tan??? ) to the curve at the point ?? . This is also said to give the slope of the curve at the point ?? Page 3 APPLICATION OF DERIVATIVES The notion of derivatives was introduced to solve problems of physics concerning motion of an object. The velocity of an object is a measure of the rate of change of distance with respect to time. Acceleration is a measure of the rate of change of velocity with respect to time. This rate of change is precisely given by the notion of derivative. The derivative is also used to find the equation of tangent to a curve at a specific point. TANGENT AND NORMAL Let ?? =?? (?? ) be the equation of a curve. At a point ?? , on the curve, the value of ???? ???? (if defined) gives the slope the tangent (=tan??? ) to the curve at the point ?? . This is also said to give the slope of the curve at the point ?? TANGENT AND NORMAL (i) Equation of tangent at point ?? (?? 1 ,?? 1 ) to the curve ?? =?? (?? ) is given by the equation : ?? -?? 1 =( ???? ???? ) (?? 1 ,?? 1 ) (?? -?? 1 ) where ( ???? ???? ) (?? 1 ,?? 1 ) denotes value of ???? ???? at the point (?? 1 ,?? 1 ) . Page 4 APPLICATION OF DERIVATIVES The notion of derivatives was introduced to solve problems of physics concerning motion of an object. The velocity of an object is a measure of the rate of change of distance with respect to time. Acceleration is a measure of the rate of change of velocity with respect to time. This rate of change is precisely given by the notion of derivative. The derivative is also used to find the equation of tangent to a curve at a specific point. TANGENT AND NORMAL Let ?? =?? (?? ) be the equation of a curve. At a point ?? , on the curve, the value of ???? ???? (if defined) gives the slope the tangent (=tan??? ) to the curve at the point ?? . This is also said to give the slope of the curve at the point ?? TANGENT AND NORMAL (i) Equation of tangent at point ?? (?? 1 ,?? 1 ) to the curve ?? =?? (?? ) is given by the equation : ?? -?? 1 =( ???? ???? ) (?? 1 ,?? 1 ) (?? -?? 1 ) where ( ???? ???? ) (?? 1 ,?? 1 ) denotes value of ???? ???? at the point (?? 1 ,?? 1 ) . TANGENT AND NORMAL (ii) Equation of normal at point ?? (?? 1 ,?? 1 ) (by definition, normal is a line ? to a tangent at ?? ) is given by ?? -?? 1 = ( -1 ( ???? ???? ) (?? 1 ,?? 1 ) (?? -?? 1 )?( here, ( ???? ???? ) ?? ?0) or (?? -?? 1 )+( ???? ???? ) (?? 1 ,?? 1 ) (?? -?? 1 )=0 Page 5 APPLICATION OF DERIVATIVES The notion of derivatives was introduced to solve problems of physics concerning motion of an object. The velocity of an object is a measure of the rate of change of distance with respect to time. Acceleration is a measure of the rate of change of velocity with respect to time. This rate of change is precisely given by the notion of derivative. The derivative is also used to find the equation of tangent to a curve at a specific point. TANGENT AND NORMAL Let ?? =?? (?? ) be the equation of a curve. At a point ?? , on the curve, the value of ???? ???? (if defined) gives the slope the tangent (=tan??? ) to the curve at the point ?? . This is also said to give the slope of the curve at the point ?? TANGENT AND NORMAL (i) Equation of tangent at point ?? (?? 1 ,?? 1 ) to the curve ?? =?? (?? ) is given by the equation : ?? -?? 1 =( ???? ???? ) (?? 1 ,?? 1 ) (?? -?? 1 ) where ( ???? ???? ) (?? 1 ,?? 1 ) denotes value of ???? ???? at the point (?? 1 ,?? 1 ) . TANGENT AND NORMAL (ii) Equation of normal at point ?? (?? 1 ,?? 1 ) (by definition, normal is a line ? to a tangent at ?? ) is given by ?? -?? 1 = ( -1 ( ???? ???? ) (?? 1 ,?? 1 ) (?? -?? 1 )?( here, ( ???? ???? ) ?? ?0) or (?? -?? 1 )+( ???? ???? ) (?? 1 ,?? 1 ) (?? -?? 1 )=0 TANGENT AND NORMAL (iii) Angle between two curves : Let ?? =?? (?? ) and ?? =?? (?? ) be the equation of two curves intersecting at point ?? (?? 1 ,?? 1 ) . Then the angle between curves ?? =?? (?? ) and ?? =?? (?? ) at their point of intersection ?? is defined as the angle ?? between the tangents ?? ?? and ?? ?? to the curves ?? =?? (?? ) and ?? =?? (?? ) respectively at their point of intersection.Read More
FAQs on Flashcards: Application of Derivatives
| 1. How do I find maximum and minimum values using derivatives for JEE? |  |
Ans. To find extrema, calculate the first derivative, set it equal to zero to find critical points, then use the second derivative test-if f''(x) > 0, it's a minimum; if f''(x) < 0, it's maximum. This method, called optimisation, is fundamental for solving application of derivatives problems. Alternatively, evaluate the function at critical points and endpoints to compare values directly.
| 2. What's the difference between increasing and decreasing functions in calculus? | |
Ans. A function is increasing when its first derivative f'(x) > 0 across an interval, meaning values rise as x increases. Conversely, it's decreasing when f'(x) < 0, indicating values fall. Identifying these intervals using derivative sign analysis helps determine function behaviour and is crucial for sketching curves and solving rate of change problems in JEE.
| 3. How do I solve rate of change problems using derivatives? | |
Ans. Rate of change refers to how quickly one quantity changes relative to another, calculated using the first derivative. For related rates, establish a relationship between variables, differentiate with respect to time, then substitute known values. This technique solves real-world problems like water draining from tanks or shadows lengthening-common JEE application-based questions requiring conceptual understanding rather than memorisation.
| 4. Why do I need to check the second derivative test for critical points? | |
Ans. The second derivative test distinguishes between local maxima, minima, and saddle points at critical locations. When f'(x) = 0, the second derivative reveals concavity: f''(x) > 0 indicates concave-up (minimum), f''(x) < 0 indicates concave-down (maximum). If f''(x) = 0, further investigation is needed. This confirmation step prevents incorrectly classifying stationary points during optimisation problems.
| 5. How are tangent and normal lines connected to derivatives in coordinate geometry? | |
Ans. The derivative at a point gives the slope of the tangent line; the normal line is perpendicular to it. For a curve y = f(x) at point (a, f(a)), tangent slope equals f'(a), and normal slope equals -1/f'(a). Writing equations of tangents and normals using point-slope form combines differentiation with geometry-a frequently tested application combining curve analysis and algebraic manipulation.
About this Document
3.2K Views
4.73/5 Rating
Apr 29, 2026 Last updated
Document Description: Flashcards: Application of Derivatives for JEE 2026 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The notes and questions for Flashcards: Application of Derivatives have been prepared according to the JEE exam syllabus. Information about Flashcards: Application of Derivatives covers topics like and Flashcards: Application of Derivatives Example, for JEE 2026 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Flashcards: Application of Derivatives.
Introduction of Flashcards: Application of Derivatives in English is available as part of our Mathematics (Maths) for JEE Main & Advanced for JEE & Flashcards: Application of Derivatives in Hindi for Mathematics (Maths) for JEE Main & Advanced course. Download more important topics related with notes, lectures and mock test series for JEE Exam by signing up for free. JEE: Flashcards: Application of Derivatives
Description
Flashcards: Application of Derivatives of Maths covers all the important topics, helping you prepare for the JEE exam on EduRev. Start for free!
Information about Flashcards: Application of Derivatives
In this doc you can find the meaning of Flashcards: Application of Derivatives defined & explained in the simplest way possible. Besides explaining types of Flashcards: Application of Derivatives theory, EduRev gives you an ample number of questions to practice Flashcards: Application of Derivatives tests, examples and also practice JEE tests
Related Searches
Flashcards: Application of Derivatives, study material, Important questions, Free, pdf , Flashcards: Application of Derivatives, mock tests for examination, Viva Questions, video lectures, shortcuts and tricks, Extra Questions, Sample Paper, Objective type Questions, Exam, MCQs, Summary, Semester Notes, past year papers, Previous Year Questions with Solutions, ppt, practice quizzes, Flashcards: Application of Derivatives;