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AP EAMCET20227 Jul 2022Morning ShiftMathematicsApplication of DerivativesActual

The perimeter of a sector is constant. If its area is to be maximum, the sectorical angle should be

Options

  1. A^c 6
  2. B^c 4
  3. C4^C
  4. D2^c

Correct answer

D. 2^c

Step-by-step solution

Perimeter, P=2 r+r =r(2+ ) According to question, r(2+ )=k r= k +2 Let A be the area to the sector A= 1 2 r^2 = k^2 2 ( +2)^2 d A d = k^2 2 [ ( +2)^2 1- 2( +2) ( +2)^4 ]= k^2 2 (2- ) (2+ )^3 For maximum area, d A d =0 =2 [ d^2 A d ^2 ] < 0 =2 A is maximum, when =2^c

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