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Question 27 According to a psychologist, the ability of a person to understand spatial concepts is given by ๐ด=1/3 โˆš๐‘ก, where ๐‘ก is the age in years, ๐‘กโˆˆ[5, 18]. Show that the rate of increase of the ability to understand spatial concepts decreases with age in between 5 and 18 .Given ๐ด=1/3 โˆš๐‘ก We need to show that the rate of increase of the ability to understand spatial concepts decreases with age in between 5 and 18 Thus, we need to show Rate of increase in ability is decreasing in [5, 18] i.e. R is decreasing in [5, 18] i.e. Rโ€™ < 0 in [๐Ÿ“, ๐Ÿ๐Ÿ–] Now, Rate of increase in ability = ๐๐‘จ/๐’…๐’• = ๐‘‘(1/3 โˆš๐‘ก)/๐‘‘๐‘ก = ๐Ÿ/๐Ÿ‘ ร— ๐’…(โˆš๐’•)/๐’…๐’• = 1/3 ร—1/(2โˆš๐‘ก) = ๐Ÿ/(๐Ÿ”โˆš๐’•) And, Rโ€™ = ๐’…/๐’…๐’•(๐’…๐‘จ/๐’…๐’•) Rโ€™ = ๐‘‘(1/(6โˆš๐‘ก))/๐‘‘๐‘ก Rโ€™ = ๐Ÿ/๐Ÿ” ๐’…(๐Ÿ/โˆš๐’•)/๐’…๐’• Rโ€™ = 1/6 ๐‘‘(๐‘ก^(โˆ’1/2) )/๐‘‘๐‘ก Rโ€™ = 1/6 ร— โˆ’1/2 ๐‘ก^(โˆ’1/2โˆ’1) Rโ€™ = (โˆ’๐Ÿ)/๐Ÿ๐Ÿ ๐’•^(โˆ’๐Ÿ‘/๐Ÿ) Now, for t in [5, 18] Rโ€™ < 0 Thus, Rate of increase in ability is decreasing in [5, 18]

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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, Social Science, Physics, Chemistry, Computer Science at Teachoo.