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
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 You are here
Misc 3 Important
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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 33 Find intervals in which the function given by f(đĽ) =3/10 đĽ4 â 4/5 đĽ^3â 3đĽ2 + 36/5 đĽ + 11 is (a) strictly increasing (b) strictly decreasingf(đĽ) = 3/10 đĽ4 â 4/5 đĽ^3â 3đĽ2 + 36/5 đĽ + 11 Finding fâ(đ) fâ(đĽ) = 3/10 Ă 4đĽ^3 â 4/5 Ă 3đĽ^2 â 3 Ă 2x + 36/5 + 0 fâ(đĽ) = 12/10 đĽ^3â 12/5 đĽ^2â 6x + 36/5 fâ(đĽ) = 6/5 đĽ^3â 12/5 đĽ^2â 6x + 36/5 fâ(đĽ) = 6(đĽ^3/5â(2đĽ^2)/5âđĽ+6/5) fâ(đĽ) = 6((đĽ^3 â 2đĽ^2â 5đĽ + 6)/5) = 6/5 (đĽ^3â2đĽ^2â5đĽ+6) = 6/5 (đĽâ1)(đĽ2âđĽâ6) = 6/5 (đĽâ1)(đĽ2â3đĽ+2đĽâ6) = 6/5 (đĽâ1)[đĽ(đĽâ3)+2(đĽâ3)] = 6/5 (đĽâ1)(đĽ+2)(đĽâ3) Hence, fâ(đ) = đ/đ (đâđ)(đ+đ)(đâđ) Putting fâ(đ) = 0 đ/đ (đâđ)(đ+đ)(đâđ) = 0 fâ(đĽ) = 6((đĽ^3 â 2đĽ^2â 5đĽ + 6)/5) = 6/5 (đĽ^3â2đĽ^2â5đĽ+6) = 6/5 (đĽâ1)(đĽ2âđĽâ6) = 6/5 (đĽâ1)(đĽ2â3đĽ+2đĽâ6) = 6/5 (đĽâ1)[đĽ(đĽâ3)+2(đĽâ3)] = 6/5 (đĽâ1)(đĽ+2)(đĽâ3) Hence, fâ(đ) = đ/đ (đâđ)(đ+đ)(đâđ) Putting fâ(đ) = 0 đ/đ (đâđ)(đ+đ)(đâđ) = 0 (đĽâ1)(đĽ+2)(đĽâ3) = 0 Hence, x = â2 , 1 & 3 Plotting points on number line Hence, f(đĽ) is strictly decreasing on the interval đĽ â (ââ,âđ)& (đ , đ) f(đĽ) is strictly increasing on the interval đĽ â (âđ,đ) & (đ , â)