Last updated at Aug. 19, 2021 by Teachoo

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Ex 6.5,1 (Method 1) Find the maximum and minimum values, if any, of the following functions given by (iv) f(๐ฅ) = ๐ฅ3 + 1f(๐ฅ)=๐ฅ^3+1 Finding fโ(x) fโ(๐ฅ)=๐(๐ฅ^3 + 1)/๐๐ฅ =3๐ฅ^2 Putting fโ(๐)=๐ 3๐ฅ^2=0 ๐ฅ^2=0 ๐ฅ=0 Therefore by first derivate test, the point ๐ฅ=0 is neither a point of local maxima nor a point of local Minima Hence ๐=๐ is point of inflexion Hence, there is no minimum or maximum value Ex 6.5, 1 (Method 2) Find the maximum and minimum values, if any, of the following functions given by (iv) f(๐ฅ) = ๐ฅ3 + 1 ๐ฅ=0 Finding fโโ(x) fโ(x) = 3x2 fโโ(x) = 6x Finding fโโ(x) at x = 0 fโโ(0) = 6 ร 0 = 0 Since fโโ(x) = 0 at x = 0 โด The point ๐ฅ=0 is neither a point of local maxima nor a point of local Minima Hence ๐=๐ is point of inflexion Hence, there is no minimum or maximum value

Ex 6.5

Ex 6.5, 1 (i)
Important

Ex 6.5, 1 (ii)

Ex 6.5, 1 (iii) Important

Ex 6.5, 1 (iv) You are here

Ex 6.5, 2 (i)

Ex 6.5, 2 (ii) Important

Ex 6.5, 2 (iii)

Ex 6.5, 2 (iv) Important

Ex 6.5, 2 (v) Important

Ex 6.5, 3 (i)

Ex 6.5, 3 (ii)

Ex 6.5, 3 (iii)

Ex 6.5, 3 (iv) Important

Ex 6.5, 3 (v)

Ex 6.5, 3 (vi)

Ex 6.5, 3 (vii) Important

Ex 6.5, 3 (viii)

Ex 6.5, 4 (i)

Ex 6.5, 4 (ii) Important

Ex 6.5, 4 (iii)

Ex 6.5, 5 (i)

Ex 6.5, 5 (ii)

Ex 6.5, 5 (iii) Important

Ex 6.5, 5 (iv)

Ex 6.5,6

Ex 6.5,7 Important

Ex 6.5,8

Ex 6.5,9 Important

Ex 6.5,10

Ex 6.5,11 Important

Ex 6.5,12 Important

Ex 6.5,13

Ex 6.5,14 Important

Ex 6.5,15 Important

Ex 6.5,16

Ex 6.5,17

Ex 6.5,18 Important

Ex 6.5,19 Important

Ex 6.5, 20 Important

Ex 6.5,21

Ex 6.5,22 Important

Ex 6.5,23 Important

Ex 6.5,24 Important

Ex 6.5,25 Important

Ex 6.5,26 Important

Ex 6.5, 27 (MCQ)

Ex 6.5,28 (MCQ) Important

Ex 6.5,29 (MCQ)

Chapter 6 Class 12 Application of Derivatives (Term 1)

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.