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MHT CET20228 Aug 2022Evening ShiftMathematicsApplication of DerivativesActual

Let A D and B C be two vertical poles at A and B respectively on a horizontal ground. If A D=8 ~m , B C=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

Options

  1. A8
  2. B5
  3. C4
  4. D7

Correct answer

B. 5

Step-by-step solution

aligned & f(x)=M D^2+M C^2 & f(x)=x^2+8^2+(10-x)^2+11^2 & f^ (x)=2 x-2(10-x) & f^ (x)=4 x-20 & for f(x) to be minimum x=5 aligned

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