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MHT CET202122 Sep 2021Evening ShiftMathematicsApplication of DerivativesActual

If f(x)=x^2+a x+b has minima at x=3 whose value is 5 , then the values of a and b are respectively.

Options

  1. A-6,-14
  2. B-6,14
  3. C14,-6
  4. D6,14

Correct answer

B. -6,14

Step-by-step solution

f(x)=x^2+a x+b f ^ ( x )=2 x + a and when f ^ ( x )=0 , we get x = - a 2 Now f ^ ( x )=2 and 2>0 f ( x ) has minima at x = - a 2 =3 [as per given data] a =-6 Since Minimum value of f(x) is 5 at x=3 , we write 5=(3)^2+(-6)(3)+b b=14

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