Chapter 6 Class 12 Application of Derivatives
Question 7 Important Deleted for CBSE Board 2025 Exams
Question 12 Deleted for CBSE Board 2025 Exams
Question 15 Important Deleted for CBSE Board 2025 Exams
Question 26 (MCQ) Important Deleted for CBSE Board 2025 Exams
Example 23 Important
Example 25 Important
Example 26 Important
Example 28 Important You are here
Ex 6.3, 1 (i) Important
Ex 6.3, 5 (i)
Ex 6.3,7 Important
Ex 6.3,11 Important
Ex 6.3,18 Important
Ex 6.3, 20 Important
Ex 6.3,23 Important
Ex 6.3, 26 Important
Ex 6.3,28 (MCQ) Important
Question 14 Important Deleted for CBSE Board 2025 Exams
Example 33 Important
Misc 3 Important
Misc 8 Important
Misc 10 Important
Misc 14 Important
Question 6 (MCQ) Deleted for CBSE Board 2025 Exams
Chapter 6 Class 12 Application of Derivatives
Last updated at April 16, 2024 by Teachoo
Example 28 Find absolute maximum and minimum values of a function f given by f (đĽ) = ă12 đĽă^(4/3) â ă 6đĽă^(1/3) , đĽ â [ â 1, 1] f (đĽ) = ă12 đĽă^(4/3) â ă 6đĽă^(1/3) Finding fâ(đ) fâ(đĽ)=đ(12đĽ^(4/3) â 6đĽ^(1/3) )/đđĽ = 12 Ă 4/3 đĽ^(4/3 â1)â6 Ă 1/3 đĽ^(1/3 â1) = 4 Ă 4 đĽ^((4 â 3)/3) â2đĽ^((1 â 3)/3) = 16 đĽ^(1/3) â2đĽ^((â2)/3) = 16 đĽ^(1/3) â 2/đĽ^(2/3) = (16đĽ^(1/3) Ă đĽ^(2/3) â 2)/đĽ^(2/3) = (16đĽ^(1/3 + 2/3) â 2)/đĽ^(2/3) = (16đĽ^(3/3) â 2)/đĽ^(2/3) = (16đĽ â 2)/đĽ^(2/3) = đ(đđ â đ)" " /đ^(đ/đ) Hence, fâ(đĽ)=2(8đĽ â 1)/đĽ^(2/3) Putting fâ(đ)=đ 2(8đĽ â 1)/đĽ^(2/3) =0 2(8đĽâ1)=0 ĂđĽ^(2/3) 2(8đĽâ1)=0 8đĽâ1= 0 8đĽ=1 đ=đ/đ Note that: Since fâ(đĽ)=2(8đĽ â 1)/đĽ^(2/3) fâ(đĽ) is not defined at đ= 0 đ=đ/đ & 0 are critical points Since, we are given interval [âđ , đ] Hence calculating f(đĽ) at đĽ=âđ, 0, 1/8, đ Hence, Absolute maximum value of f(x) is 18 at đ = â1 & Absolute minimum value of f(x) is (âđ)/đ at đ = đ/đ