# Ex 6.5,15 - 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 6.5,15 (Method 1) Find two positive numbers and such that their sum is 35 and the product 2 5 is a maximum. Given two number are & Such that + = 35 = 35 Let P = 2 5 We need to maximise P Step 1: Finding P P = 2 5 P = 2 35 5 P = 2 35 5 P = 2 . 35 5 + 35 5 . 2 =2 . 35 5 + 5 35 4 . 35 . 2 =2 . 35 5 + 5 35 4 . 0 1 2 =2 . 35 5 + 5 35 4 2 =2 35 5 5 2 35 4 = 35 4 2 35 5 = 35 4 70 7 Step 2: Putting P =0 35 4 70 7 =0 Hence = 0 , 10 , 35 are Critical Points But, If We Take = 0 Product will be 0 So, x = 0 is not possible If x = 35 = 35 35 = 35 35 = 0 So, product will be 0 So, x = 35 is not possible Hence only critical point is =10 Step 3: Finding P P = 35 4 70 7 P = 35 4 70 7 2 P = 35 4 . 70 7 2 + 70 7 2 35 4 =4 35 3 . 35 . 70 7 2 + 70 14 35 4 =4 35 3 0 1 70 7 2 + 70 14 35 4 = 4 35 3 70 7 2 + 70 14 35 4 Putting = 10 P at = 10 = 4 35 10 3 70 10 7 10 2 + 70 14 10 35 10 4 = 4 25 3 700 700 + 70 140 25 4 = 4 25 3 0 + 70 25 4 =0 70 25 4 = 70 25 4 < 0 Thus P <0 when = 10 P is maximum when = 10 Thus, when = 10 = 35 = 35 10=25 Hence = 10 & = 25 Ex 6.5,15 (Method 2) Find two positive numbers and such that their sum is 35 and the product 2 5 is a maximum. Given two number are & Such that + = 35 = 35 Let P = 2 5 We need to maximise P Step 1: Finding P P = 2 5 P = 2 35 5 P = 2 35 5 P = 2 . 35 5 + 35 5 . 2 =2 . 35 5 + 5 35 4 . 35 . 2 =2 . 35 5 + 5 35 4 . 0 1 2 =2 . 35 5 + 5 35 4 2 =2 35 5 5 2 35 4 = 35 4 2 35 5 = 35 4 70 7 Step 2: Putting P =0 35 4 70 7 =0 35 4 70 7 =0 Hence = 0 , 10 , 35 are Critical Points But, If We Take = 0 Product will be 0 So, x = 0 is not possible If x = 35 = 35 35 = 35 35 = 0 So, product will be 0 So, x = 35 is not possible Hence only critical point is =10 Step 3: = 10 is point of maxima P is maximum at = 10 Thus, when = 10 = 35 = 35 10=25 Hence = 10 & = 25

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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.