Application of Derivatives CBSE Class 12 Maths C- 6 Revision Notes

Application of Derivatives CBSE Class 12 Maths Chapter 6 Revision Notes

By Team Aakash Byju's

It is advised that students should revise the chapter ‘Application of Derivatives’ as many times as possible because it is one of the highest marks carrying chapters.

[{"selector":"#anim-8687d7d0-f424-4300-b923-3b9c90ef984f","keyframes":{"transform":["translate3d(-115.2381%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1300,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-7a9ff76c-dd1a-47dc-a508-791febc74144","keyframes":{"opacity":[0,1]},"delay":0,"duration":1300,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-e8e02967-3955-4e0b-9773-40d574fc9c9e","keyframes":{"transform":["scale(0.15)","scale(1)"]},"delay":0,"duration":1300,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"forwards"}]

Click Here To Attend Free Trail Class

[{"selector":"#anim-04c0408a-8096-407d-a6d4-6959c3594d9f","keyframes":[{"offset":0,"transform":"translate3d(0, -707.778%, 0)","easing":"cubic-bezier(.5, 0, 1, 1)"},{"offset":0.29,"transform":"translate3d(0, 0%, 0)","easing":"cubic-bezier(0, 0, .5, 1)"},{"offset":0.45,"transform":"translate3d(0, -199.0271736%, 0)","easing":"cubic-bezier(.5, 0, 1, 1)"},{"offset":0.61,"transform":"translate3d(0, 0%, 0)","easing":"cubic-bezier(0, 0, .5, 1)"},{"offset":0.71,"transform":"translate3d(0, -67.6635768%, 0)","easing":"cubic-bezier(.5, 0, 1, 1)"},{"offset":0.8,"transform":"translate3d(0, 0%, 0)","easing":"cubic-bezier(0, 0, .5, 1)"},{"offset":0.85,"transform":"translate3d(0, -25.409230200000003%, 0)","easing":"cubic-bezier(.5, 0, 1, 1)"},{"offset":0.92,"transform":"translate3d(0, 0%, 0)","easing":"cubic-bezier(0, 0, .5, 1)"},{"offset":0.96,"transform":"translate3d(0, -11.0413368%, 0)","easing":"cubic-bezier(.5, 0, 1, 1)"},{"offset":1,"transform":"translate3d(0, 0%, 0)","easing":"cubic-bezier(0, 0, .5, 1)"}],"delay":0,"duration":1300,"fill":"both"}] Download Aakash APP

Learn the definition of the Rate of Change of Quantities and know when it is positive and negative.

[{"selector":"#anim-603a6301-ae53-4456-85d3-1f2ae891dd7c","keyframes":{"transform":["translate3d(-115.2381%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1300,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-eb7de2fd-ab0a-485a-a394-19592242fc6b","keyframes":{"opacity":[0,1]},"delay":0,"duration":1300,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-3c8801b6-1728-40ba-b7cb-04e6083dfb78","keyframes":{"transform":["scale(0.15)","scale(1)"]},"delay":0,"duration":1300,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"forwards"}]

Add notes about ‘Marginal Cost’ and ‘Marginal Revenue’ , learn how to express them and know the terms used in their expressions.

[{"selector":"#anim-b480dabb-ef40-4a18-b5bc-1f122473e54c","keyframes":{"transform":["translate3d(-115.14196%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1300,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-dfb6a29e-0cc2-4f60-94cf-8a6cb15aba96","keyframes":{"opacity":[0,1]},"delay":0,"duration":1300,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"both"}] [{"selector":"#anim-94d7d27a-61f8-429a-aa1b-920261b3a1c5","keyframes":{"transform":["scale(0.15)","scale(1)"]},"delay":0,"duration":1300,"easing":"cubic-bezier(0.4, 0.4, 0.0, 1)","fill":"forwards"}]

Learn when a function f(x) is

[{"selector":"#anim-d8920358-1e29-47ae-b1c6-99fa621b6e93","keyframes":{"opacity":[0,1]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"both"}] [{"selector":"#anim-c5a07650-88e7-4466-b286-2035b664ab34","keyframes":{"transform":["scale(0.3333333333333333)","scale(1)"]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}] [{"selector":"#anim-5496f702-4ee9-47cd-8eb7-f0a46ff6080d","keyframes":{"opacity":[0,1]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"both"}] [{"selector":"#anim-091d4247-38de-454b-9d05-325fbb2c9486","keyframes":{"transform":["scale(0.3333333333333333)","scale(1)"]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}]

Learn what is ‘Monotonic Function’ and ‘Approximation’.

[{"selector":"#anim-9125f21b-7874-41df-a20e-bdcbcbdf394b","keyframes":{"opacity":[0,1]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"both"}] [{"selector":"#anim-64f2e5bf-fd8a-4f30-b9bf-125d3d102c68","keyframes":{"transform":["scale(0.3333333333333333)","scale(1)"]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}]

Study about ‘Equations of Tangent and Normal’ and learn

[{"selector":"#anim-59eef800-100f-4709-804d-f855449215f5","keyframes":{"opacity":[0,1]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"both"}] [{"selector":"#anim-1f206c0a-5ef8-49e4-aef7-2d9de06aa39f","keyframes":{"transform":["scale(0.3333333333333333)","scale(1)"]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}] [{"selector":"#anim-d8b1f848-5cb3-46c1-8d1c-606aeaeaf824","keyframes":{"opacity":[0,1]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"both"}] [{"selector":"#anim-8cdd0013-e604-4f3b-8f15-06f037094c8d","keyframes":{"transform":["scale(0.3333333333333333)","scale(1)"]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}]

Add notes about Maximum and Minimum Value and Local Maxima and Local Minima.

[{"selector":"#anim-dfe22a87-120e-4799-ab09-dbea974d1858","keyframes":{"opacity":[0,1]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"both"}] [{"selector":"#anim-633bd174-ab08-4247-818f-73b3087e2502","keyframes":{"transform":["scale(0.3333333333333333)","scale(1)"]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}]

Also, learn the topic ‘Point of Inflection’ and two cases under it

[{"selector":"#anim-9e1fe298-fd42-4c93-bc2d-6bd373c18576","keyframes":{"opacity":[0,1]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"both"}] [{"selector":"#anim-31c2319a-11e0-43be-beaa-586022351b62","keyframes":{"transform":["scale(0.3333333333333333)","scale(1)"]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}] [{"selector":"#anim-bd9cf710-3bf5-44b2-a1ce-49487376e939","keyframes":{"opacity":[0,1]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"both"}] [{"selector":"#anim-8a8b7826-cd8e-4763-94a3-b6d402bb5d03","keyframes":{"transform":["scale(0.3333333333333333)","scale(1)"]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}]

Know what is a ‘Critical Point’ and the verification cases for

[{"selector":"#anim-c2c4f76d-6f65-4149-bc64-e27d43ea4cc1","keyframes":{"opacity":[0,1]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"both"}] [{"selector":"#anim-61b1226e-a6bd-4be3-8671-d94d67190b11","keyframes":{"transform":["scale(0.3333333333333333)","scale(1)"]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}] [{"selector":"#anim-beaa1029-596f-43b0-94dc-5da986850077","keyframes":{"opacity":[0,1]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"both"}] [{"selector":"#anim-6dfb7644-6ac2-4b71-b476-7c94dc5cc715","keyframes":{"transform":["scale(0.3333333333333333)","scale(1)"]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}]

Finally, learn about ‘Absolute Maximum Value’ and ‘Absolute Minimum Value’.

[{"selector":"#anim-d4ebd37e-1aef-405b-b699-e09f08d51ff0","keyframes":{"opacity":[0,1]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"both"}] [{"selector":"#anim-fb6048ad-d3c5-43af-981b-9ed58f127d8c","keyframes":{"transform":["scale(0.3333333333333333)","scale(1)"]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}]

Amazing to see all the important notes of one chapter together just before you start revision, isn’t it? Share them with other students.

[{"selector":"#anim-e0dad089-8776-4833-b530-acb7b130d366","keyframes":{"opacity":[0,1]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"both"}] [{"selector":"#anim-13866d6b-65f2-451a-baf7-3d9720ce48c3","keyframes":{"transform":["scale(0.3333333333333333)","scale(1)"]},"delay":0,"duration":1300,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}]