CBSE Class 12 Sample Paper for 2023 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

## 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(đĽ) = â0.1đĽ^2 + đđĽ + 98 Putting m = 1.2 đ(đĽ) = â0.1đĽ^2 + 1.2đĽ + 98 đ(đĽ) = ăâđĽă^2/10+12đĽ/10+98 đ(đĽ) = đ/đđ(âđ^đ+đđđ+đđđ) Finding fâ(đ) đ(đĽ) = đ/đđ(âđ^đ+đđđ+đđđ) Differentiating wwr.t x đâ (đĽ) =1/10(â2đĽ+12) Putting fâ(đ) = 0 đ/đđ (âđđ+đđ)=đ â2đĽ + 12 = 0 â2đĽ = â12 đĽ = (â12)/(â2) đ =đ Finding fâ(đ) đ(đĽ) = đ/đđ(âđ^đ+đđđ+đđđ) Differentiating wwr.t x đâ (đĽ) =1/10(â2đĽ+12) Putting fâ(đ) = 0 đ/đđ (âđđ+đđ)=đ â2đĽ + 12 = 0 â2đĽ = â12 đĽ = (â12)/(â2) đ =đ Finding fââ(đ) đâ(đĽ) = 1/10(â2đĽ+12) Differentiating wr.t x đâ^â˛ (đĽ)=1/10 Ă â2 đâ^â˛ (đ)= â20 Since fââ(đĽ) < 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 , đđ] Hence, calculating f(đĽ) at đĽ = 0, 6, 12Hence, Absolute minimum value is 98 at đ=đ, đđ Absolute maximum value is 102.2 at đ=đ