RD Sharma

Solutions

Class 12 Maths

Chapter

Ex 17.2

Increasing and Decreasing Functions Ex 17.2 Q1(i)

Increasing and Decreasing Functions Ex 17.2 Q1(ii)

Increasing and Decreasing Functions Ex 17.2 Q1(iii)

Increasing and Decreasing Functions Ex 17.2 Q1(iv)

Increasing and Decreasing Functions Ex 17.2 Q1(v)

Increasing and Decreasing Functions Ex 17.2 Q1(vi)

Increasing and Decreasing Functions Ex 17.2 Q1(vii)

Increasing and Decreasing Functions Ex 17.2 Q1(viii)

Increasing and Decreasing Functions Ex 17.2 Q1(ix)

Increasing and Decreasing Functions Ex 17.2 Q1(x)

Increasing and Decreasing Functions Ex 17.2 Q1(xi)

Increasing and Decreasing Functions Ex 17.2 Q1(xii)

Increasing and Decreasing Functions Ex 17.2 Q1(xiii)

Increasing and Decreasing Functions Ex 17.2 Q1(xiv)

Increasing and Decreasing Functions Ex 17.2 Q1(xv)

Increasing and Decreasing Functions Ex 17.2 Q1(xvi)

Increasing and Decreasing Functions Ex 17.2 Q1(xvii)

p g g y g g

Increasing and Decreasing Functions Ex 17.2 Q1(xviii)

Increasing and Decreasing Functions Ex 17.2 Q1(xix)

Increasing and Decreasing Functions Ex 17.2 Q1(xx)

Increasing and Decreasing Functions Ex 17.2 Q1(xxi)

Increasing and Decreasing Functions Ex 17.2 Q1(xxii)

Increasing and Decreasing Functions Ex 17.2 Q1(xxiii)

Increasing and Decreasing Functions Ex 17.2 Q1(xxiv)

Increasing and Decreasing Functions Ex 17.2 Q1(xxv)

Increasing and Decreasing Functions Ex 17.2 Q1(xxvi)

Increasing and Decreasing Functions Ex 17.2 Q1(xxvii)

Increasing and Decreasing Functions Ex 17.2 Q1(xxviii)

Increasing and Decreasing Functions Ex 17.2 Q2

Increasing and Decreasing Functions Ex 17.2 Q3

Increasing and Decreasing Functions Ex 17.2 Q4

Increasing and Decreasing Functions Ex 17.2 Q5

Increasing and Decreasing Functions Ex 17.2 Q6

Increasing and Decreasing Functions Ex 17.2 Q7

Increasing and Decreasing Functions Ex 17.2 Q8

Increasing and Decreasing Functions Ex 17.2 Q9

Increasing and Decreasing Functions Ex 17.2 Q10

Increasing and Decreasing Functions Ex 17.2 Q11

Increasing and Decreasing Functions Ex 17.2 Q12

Increasing and Decreasing Functions Ex 17.2 Q13

Increasing and Decreasing Functions Ex 17.2 Q14

Increasing and Decreasing Functions Ex 17.2 Q15

Increasing and Decreasing Functions Ex 17.2 Q16

Increasing and Decreasing Functions Ex 17.2 Q17

Increasing and Decreasing Functions Ex 17.2 Q18

Increasing and Decreasing Functions Ex 17.2 Q19

Increasing and Decreasing Functions Ex 17.2 Q20

Increasing and Decreasing Functions Ex 17.2 Q21

Increasing and Decreasing Functions Ex 17.2 Q22

Increasing and Decreasing Functions Ex 17.2 Q23

Increasing and Decreasing Functions Ex 17.2 Q24

Increasing and Decreasing Functions Ex 17.2 Q25

Increasing and Decreasing Functions Ex 17.2 Q26

Increasing and Decreasing Functions Ex 17.2 Q27

Increasing and Decreasing Functions Ex 17.2 Q28

Increasing and Decreasing Functions Ex 17.2 Q29

Increasing and Decreasing Functions Ex 17.2 Q30

Increasing and Decreasing Functions Ex 17.2 Q31

Increasing and Decreasing Functions Ex 17.2 Q32

Increasing and Decreasing Functions Ex 17.2 Q33

Increasing and Decreasing Functions Ex 17.2 Q34

Increasing and Decreasing Functions Ex 17.2 Q35

Increasing and Decreasing Functions Ex 17.2 Q36

Increasing and Decreasing Functions Ex 17.2 Q37

Increasing and Decreasing Functions Ex 17.2 Q38

Increasing and Decreasing Functions Ex 17.2 Q39(i)

Increasing and Decreasing Functions Ex 17.2 Q39(ii)

Increasing and Decreasing Functions Ex 17.2 Q39(iii)

Consider the function1

f(x) = sinx(1+ cosx), 0 < x < ,r 2

⇒ f' ( X ) = cos X + sin X (- sin X) + cos X ( cos X)

⇒ f' (x) = cos x - sin2 x + cos2 x

⇒ f' ( x ) = cos x + ( cos2 x - 1) + cos2

x

⇒ f' ( x ) = cos x + 2 cos2 x - 1

⇒ f' ( x ) = 2 cos2 x + cos x - 1

⇒ f' ( X ) = 2 cos2 X + 2 cos X - cos X - 1⇒ f' ( X ) = 2 COS X ( COS X + 1) - 1 ( COS X + 1) ⇒ f' ( X) = (2 COS X - 1 ){ COS X + 1) For f (x) to be increasing

1 we must have

1

f' (x) > 0 ⇒ f' (x) = (2cosx - i)(cosx + 1) > 0

⇒ O<x< ,r 3

⇒xE(o,;J

So1

f (x)i sincrea sing in ( 01 ;J

For f (x) to be decreasing1

we must have1

f' (x) < 0 ⇒ f' ( X) = ( 2 COS X - 1 )( COS X + 1) < 0

,r ,r ⇒ -<x<-

3 2

⇒ XE(!!._ ,rJ 3

1

2

So1

f(x)is decreasing in (;, ;J