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JEE Main2017MathematicsApplication of DerivativesActual

The function f defined by f x = x 3 - 3 x 2 + 5 x + 7 is:

Options

  1. ADecreasing in R
  2. BIncreasing in R
  3. CIncreasing in 0 , ∞ and decreasing in - ∞ , 0
  4. DDecreasing in 0 , ∞ and increasing in - ∞ , 0

Correct answer

B. Increasing in R

Step-by-step solution

We have f x = x 3 - 3 x 2 + 5 x + 7 f ′ x = 3 x 2 - 6 x + 5 > 0       D = b 2 - 4 a c = 36 - 4 · 3 · 5 = - 14   - ve Then, f ' x > 0 .   Hence, f x is increasing in R .  

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