Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12

Last updated at Jan. 7, 2020 by Teachoo

Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12

Transcript

Ex 6.5, 2 Find the maximum and minimum values, if any, of the following functions given by (i) π (π₯)=|π₯ + 2| β1 π (π₯)=|π₯ + 2| β1 Minimum value of |π₯ + 2|=0 Minimum value of f(π₯)= minimum value of |π₯ + 2| β1 =0β1 =β1 Hence minimum value of f(π)=βπ And there is no maximum value of f(x) Ex 6.5, 2 Find the maximum and minimum values, if any, of the following functions given by (ii) π(π₯)= β | π₯ +1|+3 f(π₯)= β | π₯ +1|+3 We know that | π₯ +1|β₯0 So, β| π₯ +1|β€0 Maximum value of g(π₯) = maximum value of β | π₯ +1|+3 = 0 + 3 = 3 Hence maximum value of f(x) is 3 And there is no minimum value of f(x) Ex 6.5, 2 Find the maximum and minimum values, if any, of the following functions given by (iii) β(π₯)= sin β‘(2π₯)+ 5 β(π₯)= sin β‘(2π₯)+ 5 We know that β1 β€ sin ΞΈ β€ 1 β1 β€ sin 2π₯ β€ 1 Adding 5 both sides β1 + 5 β€ sin2π₯ + 5 β€ 1 + 5 4 β€ sin 2π₯ + 5 β€ 6 4 β€ f(π₯)β€6 Hence Maximum value of f(π)=π & Minimum value of f(π)=π Ex 6.5, 2 Find the maximum and minimum values, if any, of the following functions given by (iv) π (π₯)=|sinβ‘4π₯+3| π (π₯)=| sinβ‘4π₯+3| We know that β1 β€ sin ΞΈ β€ 1 So, β1 β€ sin 4π₯ β€ 1 Adding 3 both sides β1 + 3 β€ sin 4π₯ + 3 β€ 1 + 3 2 β€ sin 4π₯ +3 β€ 4 Taking modulus |2| β€ | sinβ‘4π₯+3| β€ |4| 2 β€ | sinβ‘4π₯+3| β€ |4| 2 β€ f(π₯)β€4 Hence Maximum value of f(π) is 4 & Minimum value of f(π) is 2 Ex 6.5, 2 Find the maximum and minimum values, if any, of the following functions given by (v) β(π₯)=π₯ + 1 , π₯ β (β1 , 1) Drawing graph of f(π₯)=π₯+1 β(π₯) have Maximum value of point closest to x = 1 & Minimum value of point closest to x = β1 but its not possible to locate such points Thus the given function has neither the maximum value nor minimum value

Ex 6.5

Ex 6.5,1
Important

Ex 6.5,2 Important You are here

Ex 6.5,3

Ex 6.5,4

Ex 6.5,5 Important

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

Ex 6.5,28 Important

Ex 6.5,29

Chapter 6 Class 12 Application of Derivatives

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.