Two runners A and B start at the origin and run along positive x -axis, with B running three times as fast as A . An observer, standing one unit above the origin, keeps A and B in view. Then the maxim

Question

Two runners A and B start at the origin and run along positive x -axis, with B running three times as fast as A . An observer, standing one unit above the origin, keeps A and B in view. Then the maximum angle of sight ' θ ' between the observes view of A and B is

TestHub · Accepted Answer

​ tan θ = tan ( θ 2 ​ − θ 1 ​ ) ⇒ tan θ = 1 + 3 x ⋅ x 3 x − x ​ = 1 + 3 x 2 2 x ​ let y = 1 + 3 x 2 2 x ​ d x d y ​ = ( 1 + 3 x 2 ) 2 2 ( 1 − 3 x 2 ) ​ d x d y ​ = 0 ⇒ x = 3 ​ 1 ​ and d x 2 d 2 y ​ = ( 1 + 3 x 2 ) 3 − 24 x ​ < 0 for x = 1/ 3 ​ ​

Mathematics - Application of Derivative Question with Solution | TestHub

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