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MHT CET2018MathematicsApplication of Derivatives

If the line y = 4 x - 5 touches to the curve y 2 = a x 3 + b at the point 2 , 3 then 7 a + 2 b =

Options

  1. A0
  2. B1
  3. C- 1
  4. D2

Correct answer

A. 0

Step-by-step solution

y 2 = a x 3 + b ⇒ 2 y d y d x = a 3 ( x 2 ) ⇒ d y d x | ( 2 , 3 ) = a ( 3 ) ( 2 ) 2 2 ( 3 ) = 2 a = Slope of tangent Since given line y = 4 x − 5 has slope m = 4 ⇒ 2 a = 4 ⇒ a = 2 Now since ( 2 , 3 ) lies on curve y 2 = a x 3 + b ⇒ ( 3 ) 2 = a ( 2 ) 3 + b ⇒ 9 = 8 a + b ⇒ 9 − 16 = b ⇒ b = − 7 So 7 a + 2 b = 7 ( 2 ) + 2 ( − 7 ) = 14 − 14 = 0

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