Question 27 - According to a psychologist, the ability of a person to

Question 27 According to a psychologist, the ability of a person to understand spatial concepts is given by 𝐴=1/3 √𝑡, where 𝑡 is the age in years, 𝑡∈[5, 18]. Show that the rate of increase of the ability to understand spatial concepts decreases with age in between 5 and 18 .Given 𝐴=1/3 √𝑡 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. R’ < 0 in [𝟓, 𝟏𝟖] Now, Rate of increase in ability = 𝐝𝑨/𝒅𝒕 = 𝑑(1/3 √𝑡)/𝑑𝑡 = 𝟏/𝟑 × 𝒅(√𝒕)/𝒅𝒕 = 1/3 ×1/(2√𝑡) = 𝟏/(𝟔√𝒕) And, R’ = 𝒅/𝒅𝒕(𝒅𝑨/𝒅𝒕) R’ = 𝑑(1/(6√𝑡))/𝑑𝑡 R’ = 𝟏/𝟔 𝒅(𝟏/√𝒕)/𝒅𝒕 R’ = 1/6 𝑑(𝑡^(−1/2) )/𝑑𝑡 R’ = 1/6 × −1/2 𝑡^(−1/2−1) R’ = (−𝟏)/𝟏𝟐 𝒕^(−𝟑/𝟐) Now, for t in [5, 18] R’ < 0 Thus, Rate of increase in ability is decreasing in [5, 18]

Question 27 - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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