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JEE Main20249 Apr 2024Morning ShiftMathematicsDifferentiationActual

Let f(x)=a x^3+b x^2+c x+41 be such that f(1)=40, f^ (1)=2 and f^ (1)=4 . Then a ^2+ b ^2+ c ^2 is equal to:

Options

  1. A73
  2. B62
  3. C51
  4. D54

Correct answer

C. 51

Step-by-step solution

aligned & f(x)=a x^3+b x^2+c x+41 & f^ (x)=3 a x^2+2 b x+c x & f^ (1)=3 a+2 b+c=2 (1) aligned aligned & f ^ ( n )=6 ax +2 ~b & f ^ (1)=6 a +2 ~b =4 & 3 a + b =2 .(2) aligned aligned & (1)-(2) & b+c=0...(3) aligned aligned & f (1)=40 & a + b + c +41=40 aligned use (3) a+41=40 by (2) aligned & -3+b=2 b=5 & c=-5 & a^2+b^2+c^2=1+25+25=51 aligned

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