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MHT CET202314 May 2023Evening ShiftMathematicsApplication of DerivativesActual

Let P (x) be a polynomial of degree 2 , with P (2)=-1, P ^ (2)=0, P ^ (2)=2 , then P (1.001) is

Options

  1. A0.002
  2. B-0.002
  3. C0.004
  4. D-0.004

Correct answer

B. -0.002

Step-by-step solution

aligned & Let P (x)= a x^2+ b x+ c & P ^ (x)=2 a x+ b & P ^ (x)=2 a & P ^ (2)=2 a & 2=2 a & a =1 & P ^ (2)=2 a (2)+ b & 0=4 a + b & 0=4(1)+ b & b =-4 & P (2)= a (2)^2+ b (2)+ c & -1=4 a +2 ~b + c & -1=4(1)+2(-4)+ c & c =3 & P (x)=x^2-4 x+3 & P ^ (x)=2 x-4 & x=1.001=1+0.001= a + h aligned Here, a =1, ~h =0.001 gathered P ( a )= P (1)=1-4+3=0 P ^ ( a )= P ^ (1)=2-4=-2 gathered P (1.001)=0+(0.001)(-2)=-0.002

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