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Manipal MET2014MathematicsApplication of Derivatives

f(x)= array cc |x^3+x^2+3 x+ x | (3+ 1 x ), & x 0 0, & x=0 array . The number of points, where f(x) attains its minimum value, is

Options

  1. A1
  2. B2
  3. C3
  4. Dinfinitely many

Correct answer

A. 1

Step-by-step solution

f(x)= aligned |x^3+x^2+3 x+ x | 0 aligned (3+ 1 x ) array l x 0 x=0 array . Let g(x)=x^3+x^2+3 x+ x aligned g^ (x) & =3 x^2+2 x+3+ x & =3 (x^2+ 2 x 3 +1 )+ x g^ (x) & =3 (x+ 1 3 )^2+ 8 9 + x 0 aligned and 2 3+ ( 1 x ) 4 Hence, minimum value of f(x) is 0 at x=0 Hence, the number of points =1

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