Example 40 - Find absolute max, min values of f(x) = 12x4/3 - Examples

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Example 40 Find absolute maximum and minimum values of a function f given by f ( ) = 12 4 3 6 1 3 , [ 1, 1] f ( ) = 12 4 3 6 1 3 Step 1: Finding f f = 12 4 3 6 1 3 = 12 4 3 4 3 1 6 1 3 1 3 1 = 4 4 4 3 3 2 1 3 3 = 16 1 3 2 2 3 = 16 1 3 2 2 3 = 16 1 3 2 3 2 2 3 = 16 1 3 + 2 3 2 2 3 = 16 3 3 2 2 3 = 16 2 2 3 = 2 8 1 2 3 Hence, f = 2 8 1 2 3 Step 2: Putting f =0 2 8 1 2 3 =0 2 8 1 =0 2 3 2 8 1 =0 8 1= 0 8 =1 = 1 8 Note that: Since f = 2 8 1 2 3 f is not defined at = 0 = 1 8 & 0 are critical points Step 3: We are given interval 1 , 1 Hence calculating f at =0, 1 8 , 1 , 1 Hence, Absolute maximum value of f(x) is 18 at = 1 & Absolute minimum value of f(x) is 9 4 at =

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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.