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For f x = x 3 + b x 2 + c x + d , if b 2 > 4 c > 0 and b , c , d ∈ R , then f x

Options

  1. Ais strictly increasing
  2. Bis strictly decreasing
  3. Chas a local maxima
  4. Dis bounded

Correct answer

C. has a local maxima

Step-by-step solution

f ′ x = 3 x 2 + 2 b x + c Discriminant = 4 b 2 - 3 c > 4 c > 0 (as c > 0 ) Hence, f x has a local maxima and a local minima

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