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AP EAMCET20227 Jul 2022Morning ShiftMathematicsApplication of DerivativesActual

Let f(x)=x^2+ 1 x^2 and g(x)=x- 1 x for x R- -1,0,+1 , then the local minimum of f(x) g(x) is

Options

  1. A-3
  2. B2 2
  3. C-2 2
  4. D3

Correct answer

B. 2 2

Step-by-step solution

f(x)=x^2+ 1 x^2 = (x- 1 x )+2, g(x)=x- 1 x Let x- 1 x =tf(x)=t^2+2, g(x)=t aligned & f(x) g(x) =t+ 2 t =h(t) & h^ (t)=1- 2 t^2 aligned On putting h^ (t)=0 aligned & & 1- 2 t^2 & =0 & & t & = 2 & & h^ (t) & = 4 t^3 aligned h^ (- 2 ) 0 t= 2 is a point of minima. Local minimum value of h(t)= 2 + 2 2 =2 2 Required local minimum value =2 2

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