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MHT CET202313 May 2023Morning ShiftMathematicsApplication of DerivativesActual

If f (x)=x^3+ b x^2+ c x+ d and 0 < b ^2 < c , then in (- , )

Options

  1. Af (x) has a local maxima.
  2. Bf (x) is strictly increasing function.
  3. Cf (x) is bounded.
  4. Df (x) is strictly decreasing function.

Correct answer

B. f (x) is strictly increasing function.

Step-by-step solution

aligned & f (x)=x^3+ b x^2+ c x+ d & f ^ (x)=3 x^2+2 ~b x+ c aligned Now its discriminant =4 (b^2-3 c ) 4 ( ~b ^2- c )-8 c 0 f ^ (x)>0 for all x R f is strictly increasing on R .

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