Question 36 (iii) (Choice 2) - CBSE Class 12 Sample Paper for 2023 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by Teachoo

Find the points of local maximum/local minimum, if any, in the interval (0, 12) as well as the points of absolute maximum/absolute minimum in the interval [0, 12]. Also, find the corresponding local maximum/local minimum and the absolute maximum/absolute minimum values of the function.

Transcript

Question 36 (iii) - Choice 2 Find the points of local maximum/local minimum, if any, in the interval (0, 12) as well as the points of absolute maximum/absolute minimum in the interval [0, 12]. Also, find the corresponding local maximum/local minimum and the absolute maximum/absolute minimum values of the function.Now, our function
đ(đĽ) = â0.1đĽ^2 + đđĽ + 98
Putting m = 1.2
đ(đĽ) = â0.1đĽ^2 + 1.2đĽ + 98
đ(đĽ) = ăâđĽă^2/10+12đĽ/10+98
đ(đĽ) = đ/đđ(âđ^đ+đđđ+đđđ)
Finding fâ(đ)
đ(đĽ) = đ/đđ(âđ^đ+đđđ+đđđ)
Differentiating wwr.t x
đâ (đĽ) =1/10(â2đĽ+12)
Putting fâ(đ) = 0
đ/đđ (âđđ+đđ)=đ
â2đĽ + 12 = 0
â2đĽ = â12
đĽ = (â12)/(â2)
đ =đ
Finding fâ(đ)
đ(đĽ) = đ/đđ(âđ^đ+đđđ+đđđ)
Differentiating wwr.t x
đâ (đĽ) =1/10(â2đĽ+12)
Putting fâ(đ) = 0
đ/đđ (âđđ+đđ)=đ
â2đĽ + 12 = 0
â2đĽ = â12
đĽ = (â12)/(â2)
đ =đ
Finding fââ(đ)
đâ(đĽ) = 1/10(â2đĽ+12)
Differentiating wr.t x
đâ^â˛ (đĽ)=1/10 Ă â2
đâ^â˛ (đ)= â20
Since fââ(đĽ) < 0
â´ x = 6 is the local maxima
Now, finding absolute minimum and maximum values
Finding absolute minimum and maximum
Since we are given interval [đ , đđ]
Hence, calculating f(đĽ) at đĽ = 0, 6, 12Hence,
Absolute minimum value is 98 at đ=đ, đđ
Absolute maximum value is 102.2 at đ=đ

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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