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Ex 6.3
Ex 6.3, 1 (ii) You are here
Ex 6.3, 1 (iii) Important
Ex 6.3, 1 (iv)
Ex 6.3, 2 (i)
Ex 6.3, 2 (ii) Important
Ex 6.3, 2 (iii)
Ex 6.3, 2 (iv) Important
Ex 6.3, 2 (v) Important
Ex 6.3, 3 (i)
Ex 6.3, 3 (ii)
Ex 6.3, 3 (iii)
Ex 6.3, 3 (iv) Important
Ex 6.3, 3 (v)
Ex 6.3, 3 (vi)
Ex 6.3, 3 (vii) Important
Ex 6.3, 3 (viii)
Ex 6.3, 4 (i)
Ex 6.3, 4 (ii) Important
Ex 6.3, 4 (iii)
Ex 6.3, 5 (i)
Ex 6.3, 5 (ii)
Ex 6.3, 5 (iii) Important
Ex 6.3, 5 (iv)
Ex 6.3,6
Ex 6.3,7 Important
Ex 6.3,8
Ex 6.3,9 Important
Ex 6.3,10
Ex 6.3,11 Important
Ex 6.3,12 Important
Ex 6.3,13
Ex 6.3,14 Important
Ex 6.3,15 Important
Ex 6.3,16
Ex 6.3,17
Ex 6.3,18 Important
Ex 6.3,19 Important
Ex 6.3, 20 Important
Ex 6.3,21
Ex 6.3,22 Important
Ex 6.3,23 Important
Ex 6.3,24 Important
Ex 6.3,25 Important
Ex 6.3, 26 Important
Ex 6.3, 27 (MCQ)
Ex 6.3,28 (MCQ) Important
Ex 6.3,29 (MCQ)
Last updated at June 12, 2023 by Teachoo
Ex 6.3, 1 (Method 1) Find the maximum and minimum values, if any, of the following functions given by (ii) f (đĽ) = 9đĽ2+12đĽ+2Finding fâ(x) f (đĽ)=9đĽ2+12đĽ+2 Diff. w.r.t đĽ fâ(đĽ)=18đĽ+12 fâ(đĽ)=6(3đĽ+2) Putting fâ(đ)=đ 6(3đĽ+2)=0 3đĽ+2=0 3đĽ=â2 đĽ=(â2)/( 3) Hence đĽ=(â2)/3 is point of minima of f(đĽ) Finding minimum value of f(đĽ) at đĽ=(â2)/3 f(đĽ)=9đĽ^2+12đĽ+2 Putting đĽ=(â2)/3 f(đĽ)=9((â2)/3)^2+12((â2)/3)+2=9(4/3)â12(2/3)+2=â2 Thus, Minimum value of f(đ)=âđ There is no maximum value Ex 6.3, 1 (Method 2) Find the maximum and minimum values, if any, of the following functions given by (ii) f (đĽ) = 9đĽ2+12đĽ+2Finding fâ(đ) f (đĽ)=9đĽ2+12đĽ+2 Diff. w.r.t đĽ fâ(đĽ)=đ(9đĽ^2 + 12đĽ + 2)/đđĽ fâ(đĽ)=18đĽ+12 fâ(đĽ)=6(3đĽ+2) Putting fâ(đ)=đ 6(3đĽ+2)=0 3đĽ+2=0 3đĽ=â2 đĽ=(â2)/3 Finding fââ(đ) fâ(đĽ)= 6(3đĽ+2) Again diff w.r.t đĽ fââ(đĽ)=đ(6(3đĽ+2))/đđĽ fââ(đĽ)=6 đ(3đĽ + 2)/đđĽ fââ(đĽ)=6(3+0) fââ(đĽ)=6(3) fââ(đĽ)=18 So, fââ((â2)/3)=18 Since fââ(đĽ)>0 is for đĽ=(â2)/3 đĽ=(â2)/3 is point of local minima Finding minimum value Putting đĽ=(â2)/3 in f(đĽ) f (đĽ)=9đĽ2+12đĽ+2 f ((â2)/3)=9((â2)/3)^2+12((â2)/3)+2 =9(4/9)+12((â2)/3)+2 =4â8+2 =â2 Hence, minimum value = â2 There is no maximum value