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COMEDK2012MathematicsApplication of Derivatives

The function f(x)=5+36 x+3 x²-2 x³ is increasing in the interval

Options

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

Correct answer

A. (-2,3)

Step-by-step solution

Given, f(x)=5+36 x+3 x²-2 x³ f^ (x)=36+6 x-6 x²=-6 (x²-x-6 )=-6 (x²-3 x+2 x-6 )=-6(x-3)(x+2) For increasing function, f^ (x)>0 (x-3)(x+2) -2 -2 < x < 3 Hence, function f(x) is increasing in (-2,3) interval.

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