Question 37 (iii) (Choice 1) - CBSE Class 12 Sample Paper for 2023 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by Teachoo

Use First derivative Test to find the length 2x and width 2y of the soccer field (in terms of a and b) that maximize its area.

Transcript

Question 37 (iii) (Choice 1) Use First derivative Test to find the length 2x and width 2y of the soccer field (in terms of a and b) that maximize its area.Now, 𝑑𝑍/𝑑𝑥=(32𝑏^2)/𝑎^2 × (𝑎^2 𝑥−2𝑥^3) 𝒅𝒁/𝒅𝒙=(32𝑏^2)/𝑎^2 × 𝑥 × (𝒂^𝟐−𝟐𝒙^𝟐) Since 𝑑𝑍/𝑑𝑥 = changes sign from positive to negative 𝒙 = 𝒂/√𝟐 is the maxima. Thus, A is maximum at x = 𝒂/√𝟐 Finding length 2x and 2y Length = 2x = 2 × 𝑎/√2 = √𝟐a Breadth = 2y = 2 × (" " 𝒃)/𝒂 √((𝒂^𝟐 − 𝒙^𝟐 ) ) = 2b/𝑎 ×√(𝑎^2−(𝒂/√𝟐)^2 ) = 2b/𝑎 ×√(𝑎^2−𝑎^2/2) = 2b/𝑎 ×√(𝑎^2/2) = 2b/𝑎 ×𝒂/√𝟐 = 2b/√𝟐 = √𝟐 𝒃

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