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AP EAMCET202317 May 2023Morning ShiftMathematicsApplication of DerivativesActual

The function f(x)=x^2+ 54 x

Options

  1. Ais increasing and has minimum value 27 in the interval (0, )
  2. Bis decreasing and has neither maximum nor minimum in the interval (- , 0)
  3. Chas maximum value 27 in the interval (- , )
  4. Dis increasing and has neither maximum nor minimum values in the interval (- , )

Correct answer

B. is decreasing and has neither maximum nor minimum in the interval (- , 0)

Step-by-step solution

f(x)=x^2+ 54 x f^ (x)=2 x- 54 x^2 < 0 for x (- , 0) f(x) is decrasing in (- , 0) and for critical points: f^ (x)=0 2 x- 54 x^2 =0 x^3=27 x=3 So there is no critical point in (- , 0) ie f(x) has neither maximum nor minimum in (- , 0) .

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