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Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

Paragraph: Let C be the curve f(x)=( x)^2+2 x and A(a, f(a)), B(b, f(b)) where (a b) are the points of tangency of two tangents drawn from origin to the curve C Question: The value of the product ab is equal to

Options

  1. Ae
  2. B1 e
  3. Ce^2
  4. D1

Correct answer

D. 1

Step-by-step solution

aligned & y=f(x)=( x)^2+2 x & . d y d x |_ A(a, f(a)) = 2 a a + 2 a = 2 a (1+ a) aligned Also d y d x = f(a)-0 a-0 f(a) a = 2 a (1+ a) f(a)=2(1+ a) So ( a)^2+2 a=2+2 a ( a)^2=2 a=e^ 2 or e^ - 2 Hence a=e^ - 2 and b=e^ 2 So a b=1

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