Ex 5.8

Ex 5.8, 1
Deleted for CBSE Board 2022 Exams
You are here

Ex 5.8, 2 (i) Deleted for CBSE Board 2022 Exams

Ex 5.8, 2 (ii) Important Deleted for CBSE Board 2022 Exams

Ex 5.8, 2 (iii) Deleted for CBSE Board 2022 Exams

Ex 5.8, 3 Important Deleted for CBSE Board 2022 Exams

Ex 5.8, 4 Deleted for CBSE Board 2022 Exams

Ex 5.8, 5 Important Deleted for CBSE Board 2022 Exams

Ex 5.8, 6 Deleted for CBSE Board 2022 Exams

Last updated at Dec. 8, 2021 by Teachoo

Hello! Teachoo has made these pages with hours (even days!) of effort and love. Your Board exams are coming, if Teachoo has been of any help in the whole year of studying... please consider making a donation to support us.

Hello! Teachoo has made these pages with hours (even days!) of effort and love. Your Board exams are coming, if Teachoo has been of any help in the whole year of studying... please consider making a donation to support us.

Ex 5.8, 1 Verify Rolleβs theorem for the function π (π₯) = π₯2 + 2π₯ β 8, π₯ β [4, 2].Letβs check conditions of Rolleβs theorem Condition 1 We need to check if π(π₯) is continuous at [β4, 2] Since π(π)=π₯2 + 2π₯ β 8 is a polynomial & Every polynomial function is continuous for all π₯ βπ β΄ π(π₯)is continuous at π₯β[β4, 2] Conditions of Rolleβs theorem π(π₯) is continuous at [π , π] π(π₯) is derivable at (π , π) π(π) = π(π) If all 3 conditions are satisfied then there exist some c in (π , π) such that πβ²(π) = 0 Condition 2 We need to check if π(π₯) is differentiable at (β4 , 2) Since π(π) =π₯2 + 2π₯ β 8 is a polynomial . & Every polynomial function is differentiable for all π₯ βπ β΄ π(π₯) is differentiable at (β4 , 2) Condition 3 We need to check if π(π) = π(π), for a = β4, b = 2 π(βπ) π(βπ) = (β4)^2+2(β4)β8 = 16 β 8 β 8 = 0 π(π) π(π)" = " (2)^2+2(2)β8" " "= " 4+4β8" = 0" Hence, π(β4) = π(2) Now, π(π₯) = π₯2 + 2π₯ β 8" " π^β² (π) = 2π₯+2β0 π^β² (π₯) = 2π₯+2 π^β² (π) = ππ+π Since all three conditions satisfied π^β² (π) = π 2π+2 = 0 2c = β 2 c = (β2)/2 c = β1 Since c = β1 β(β4 , 2) Thus, Rolleβs Theorem is satisfied.