Example 29 - Find all points of local maxima and local minima - Local maxima and minima

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  1. Chapter 6 Class 12 Application of Derivatives
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Example 29 (Method 1) Find all points of local maxima and local minima of the function f given by ( ) = 3 3 + 3. ( )= 3 3 +3 Step 1: Finding ( ) = 3 2 3+0 = 3 2 1 Step 2: Putting = 0 3 2 1 =0 2 1=0 1 +1 =0 Thus = 1 , 1 are only critical points Step 3: Example 29(Method 2) Find all points of local maxima and local minima of the function f given by ( ) = 3 3 + 3. ( )= 3 3 +3 Step 1: Finding ( ) = 3 2 3+0 = 3 2 1 Step 2: Putting = 0 3 2 1 =0 2 1=0 1 +1 =0 So, x = 1 & x = 1 Step 3: Finding =3 2 1 =3 2 1 =3 2 0 =6 Finding maximum & minimum value of ( )= 3 3 +3 Minimum value (1)= 1 3 3 1 +3= 1 3 + 3 = 1 Maximum value ( 1)= 1 3 3 1 +3= 1 +3 + 3 = 5

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