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AP EAMCET201822 Apr 2018Morning ShiftMathematicsApplication of DerivativesActual

If y= 2 a^2-b^2 ⁻¹ [ a-b a+b x 2 ] , then . d^2 y d x^2 |_ x= 2 =

Options

  1. Ab 2 a^2
  2. Bb a^2
  3. C2 b a
  4. Db^2 2 a

Correct answer

B. b a^2

Step-by-step solution

We have, aligned & y= 2 a^2-b^2 ⁻¹ [ a-b a+b x 2 ] & d y d x = [ 2 a^2-b^2 1 1+ ( a-b a+b ) ^2 x 2 . & . a-b a+b ^2 x 2 1 2 ] & = ^2 x / 2 a+b a+b (a+b)+(a-b) ^2 x / 2 & = ^2 x / 2 a+b+a ^2 x 2 -b ^2 x / 2 & = ^2 x / 2 a (1+ ^2 x 2 )+b (1- ^2 x 2 ) & = ^2 x / 2 (1+ ^2 x 2 ) [a+b ( 1- ^2 x / 2 1+ ^2 x / 2 ) ] & d y d x = 1 a+b x & d^2 y d x^2 = -1 (a+b x)^2 (-b x) & d^2 y d x^2 = b x (a+b x)^2 & . d^2 y d x^2 |_ x= 2 = b / 2 (a+b 2 )^2 = b a^2 & aligned

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