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Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

If f(x)=x^2+x g^ (1)+g^ (2) and g(x)=f(1) x^2+x f^ (x)+f^ (x) . Then:

Options

  1. Aminimum value of f(x) is equal to -2.25
  2. Bthe value of ₂^3 d x f(x)-x+5 is equal to 4 .
  3. Cnumber of positive integral values in the domain of f(x) g(x) is 4 .
  4. Dnumber of points where g(|x|) is non derivable is 1 .

Correct answer

D. number of points where g(|x|) is non derivable is 1 .

Step-by-step solution

Put a=g^ (1), b=g^ (2)f(x)=x^2+a x+b ...(1) g(x)=c x^2+x(2 x+a)+2 g(x)=(c+2) x^2+a x+2 ...(2) g^ (x)=2(c+2) x+a array ll & g^ (1)=2(c+2)+a=a & c=-2 array g^ (x)=2(c+2) array ll & g^ (2)=2(c+2)=b & b=0 array f(x)=x^2+a xg(x)=a x+2 Now, c=f(1) array lll & f(1)=1+a=c=-2 a=-3 & f(x)=x^2-3 x, & g(x)=2-3 x array Now, verify.

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