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AP EAMCET202120 Aug 2021Evening ShiftMathematicsApplication of DerivativesActual

Find the minimum value of 2 x + 3 y when x y = 6 .

Options

  1. A9
  2. B12
  3. C8
  4. D6

Correct answer

B. 12

Step-by-step solution

Given: x y = 6 ⇒ y = 6 x ⇒ f x , y = 2 x + 3 y ⇒ f x = 2 x + 3 × 6 x ⇒ f x = 2 x + 18 x ⇒ f ' x = 2 - 18 x 2 Put f ' x = 0 for maximum or minimum ⇒ 0 = 2 - 18 x 2 ⇒ x 2 = 9 ⇒ x = ± 3 ⇒ f '' x = 0 - - 18 × 2 x 3 ⇒ f '' 3 = 36 3 3 > 0 ⇒ f '' ( 3 ) > 0 At x = 3   , f x is minimum The minimum value of f 3 = 2 3 + 3 2   = 12 .

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