# Ex 6.5,5 - Chapter 6 Class 12 Application of Derivatives

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

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Chapter 6 Class 12 Application of Derivatives

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.