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MHT CET20243 May 2024Evening 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) is strictly increasing function
  2. Bf (x) is bounded
  3. Cf (x) has a local maxima
  4. Df (x) is a strictly decreasing function

Correct answer

A. 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 , as b ^2 c and c 0 f ^ (x) 0 for all x R f is strictly increasing on R .

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