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MHT CET202124 Sep 2021Evening ShiftMathematicsApplication of DerivativesActual

The curve y=a x^3+b x^2+c x+5 touches X-axis at P(-2,0) and cuts Y -axis at a point Q , where its gradient is 3 , then

Options

  1. Aa = 1 2 , ~b = 3 4 , c =3
  2. Ba = 1 2 , ~b = -1 4 , c =-3
  3. Ca= 1 2 , b= -3 4 , c=-3
  4. Da = -1 2 , ~b = -3 4 , c =3

Correct answer

D. a = -1 2 , ~b = -3 4 , c =3

Step-by-step solution

The curve y=a x^3+b x^2+c x+5 touches X -axis at P(-2,0) 0= a (-2)^3+ b (-2)^2+ c (-2)+5 d y d x =3 a x^2+2 b x+c and at point Q on Y axis, we have d y d x =3 . Let Q (0, k) The equation (1) becomes 8 a-4 b+6=5 i.e. 8 a-4 b=-1 2 a - b = -1 4 At P (-2,0) dy dx =0 From (1), (2) & (3) a = -1 2 , ~b = -3 4 , c =3

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