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AP EAMCET201822 Apr 2018Morning ShiftMathematicsApplication of DerivativesActual

If f(x)=x^3+a x^2+b x+5 ^2 x is an increasing function on R , then

Options

  1. Aa^2-3 b-15 < 0
  2. Ba^2-3 b+15 < 0
  3. Ca^2-3 b-15>0
  4. Da^2+3 b+15>0

Correct answer

B. a^2-3 b+15 < 0

Step-by-step solution

array ll & f^ (x)>0 & 3 x^2+2 a x+b+10 x x>0 & 3 x^2+2 a x+b+5 2 x>0 & 3 x^2+2 a x+b-5>0 & 3 x^2+2 a x+(b-5)>0 Here, & a>0, a < 0 & (2 a)^2-4 3 (b-5) < 0 & 4 a^2-12(b-5) < 0 & a^2-3(b-5) < 0 & a^2-3 b+15 < 0 . array

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