# Ex 6.5,5

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 6.5,5 Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals: (i) f ( ) = 3, [ 2, 2] Step 1: Finding f f = 3 f =3 2 Step 2: Putting f =0 3 2 =0 2 =0 =0 So, =0 is critical point Step 3: Since given interval 2 , 2 Hence calculating f at = 2 , 0 , 2 Step 4: Absolute Maximum value of f(x) is 8 at = 2 & Absolute Minimum value of f(x) is 8 at = 2 Ex 6.5,5 Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals: (ii) f ( ) = sin + cos , [0, ] Step 1: Finding f f = + f = cos sin Step 2: Putting f cos sin = 0 cos = sin 1 = sin cos 1 = tan tan = 1 We know that know tan = 1 at = 4 = 4 Step 3: Since given interval 0 , Hence calculating f at =0 , 4 , Absolute Maximum value of f is at = & Absolute Minimum value of f is 1 at = Ex 6.5,5 Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals: (iii) f( ) = 4 1 2 2 , 2, 9 2 f( ) = 4 1 2 2 Step 1: Finding f f = 4 1 2 2 = 4 1 2 2 = 4 Step 2: Putting f =0 4 =0 =4 =4 is only critical point Step 3: Since given interval 2 , 9 2 Hence , calculating f at = 2 , 4 , 9 2 Absolute Maximum value of f(x) is 8 at = 4 & Absolute Minimum value of f(x) is 10 at = 2 Ex 6.5,5 Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals: (iv) f ( ) = ( 1)2 + 3, [ 3,1] f ( ) = ( 1)2 + 3 Step 1: Finding f f = 1 2 +3 = 2 1 Step 2: Putting f =0 2 1 =0 1=0 =1 Step 3: Since given interval 3 , 1 Hence , calculating f at = 3 , 1 Absolute Minimum value of f(x) is 3 at = 1 & Absolute Maximum value of f(x) is 19 at = 3

Chapter 6 Class 12 Application of Derivatives

Ex 6.3,5
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Ex 6.3,7 Important

Ex 6.3,12 Important

Ex 6.3,15 Important

Ex 6.3,26 Important

Example 35 Important

Example 37 Important

Example 38 Important

Example 40 Important

Ex 6.5,1 Important

Ex 6.5,5 Important You are here

Ex 6.5,7 Important

Ex 6.5,11 Important

Ex 6.5,18 Important

Ex 6.5,20 Important

Ex 6.5,23 Important

Ex 6.5,26 Important

Ex 6.5,28 Important

Example 46 Important

Example 47 Important

Misc 6 Important

Misc 11 Important

Misc 13 Important

Misc 17 Important

Misc 22 Important

Class 12

Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

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.