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MHT CET20239 May 2023Evening ShiftMathematicsApplication of DerivativesActual

The range of values of x for which f(x)=x^3+6 x^2-36 x+7 is increasing in

Options

  1. A(- ,-6) (2, )
  2. B(-6,2)
  3. C(- ,-2) (6, )
  4. D(-6,2]

Correct answer

A. (- ,-6) (2, )

Step-by-step solution

aligned f (x) & =x^3+6 x^2-36 x+7 f ^ (x) & =3 x^2+12 x-36 & =3 (x^2+4 x-12 ) aligned For f (x) to be increasing, aligned & f ^ (x)>0 & 3 (x^2+4 x-12 )>0 & x^2+4 x-12>0 & (x+6)(x-2)>0 & x (- ,-6) (2, ) aligned

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