         1. Chapter 6 Class 12 Application of Derivatives
2. Serial order wise
3. Ex 6.5

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

Ex 6.5 