Let A D and BC be two vertical poles at A and B respectively on a horizontal ground. If A D = 8 m , BC = 11 m and A B = 10 m , then the distance (in meters) of point M on A B from the point A such that M D 2 + M C 2 is minimum, is

Question

Let A D and BC be two vertical poles at A and B respectively on a horizontal ground. If A D = 8 m , BC = 11 m and A B = 10 m , then the distance (in meters) of point M on A B from the point A such that M D 2 + M C 2 is minimum, is, 8, 5, 4, 7

MARKS App · Accepted Answer

​ f ( x ) = M D 2 + M C 2 ⇒ f ( x ) = x 2 + 8 2 + ( 10 − x ) 2 + 1 1 2 ⇒ f ′ ( x ) = 2 x − 2 ( 10 − x ) ⇒ f ′ ( x ) = 4 x − 20 for f ( x ) to be minimum x = 5 ​

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