CBSE Class 12 Sample Paper for 2023 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

## 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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#### 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.