CBSE Class 12 Sample Paper for 2023 Boards
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CBSE Class 12 Sample Paper for 2023 Boards
Last updated at Dec. 13, 2024 by Teachoo
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
