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Question 36 (iii) (A) For what value of š’™, the volume of each container is maximum?Now, V = 2(2š‘„^3āˆ’65š‘„^2+500š‘„) And, šš•/š’…š’™= 4(š‘„āˆ’5)(3š‘„āˆ’50) Putting šš•/š’…š’™= 0 4(š‘„āˆ’5)(3š‘„āˆ’50)=0 So, x = 5 and x = šŸ“šŸŽ/šŸ‘ If š’™ = šŸ“šŸŽ/šŸ‘ Breadth of box = 25 ā€“ 2š‘„ = 25 ā€“ 2(šŸ“šŸŽ/šŸ‘) = 25 ā€“ 33.3 = ā€“8.3 Since, breadth cannot be negative, āˆ“ x = šŸ“šŸŽ/šŸ‘ is not possible Hence, š’™ = 5 only Finding Vā€™ā€™(š’™) Vā€™(š‘„)=" 4" [šŸ‘š’™^šŸāˆ’šŸ”šŸ“š’™+šŸšŸ“šŸŽ] Vā€™ā€™(š‘„)=4[6š‘„āˆ’65] Putting š’™=šŸ“ Vā€™ā€™(šŸ“)=4(6(5)āˆ’65)= 4(30āˆ’65)= 4(āˆ’35)= ā€“140 Vā€™ā€™(š’™)<šŸŽ when š‘„=5 Thus, V(š‘„) is maximum at š‘„=5 āˆ“ Square of side 5 cm is cut off from each Corner

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo