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Last updated at Aug. 19, 2021 by

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Transcript

Ex 6.5,1 (Method 1) Find the maximum and minimum values, if any, of the following functions given by (iv) f(π₯) = π₯3 + 1f(π₯)=π₯^3+1 Finding fβ(x) fβ(π₯)=π(π₯^3 + 1)/ππ₯ =3π₯^2 Putting fβ(π)=π 3π₯^2=0 π₯^2=0 π₯=0 Therefore by first derivate test, the point π₯=0 is neither a point of local maxima nor a point of local Minima Hence π=π 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(π₯) = π₯3 + 1 π₯=0 Finding fββ(x) fβ(x) = 3x2 fββ(x) = 6x Finding fββ(x) at x = 0 fββ(0) = 6 Γ 0 = 0 Since fββ(x) = 0 at x = 0 β΄ The point π₯=0 is neither a point of local maxima nor a point of local Minima Hence π=π 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)

About the Author

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.