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CUET · MATHS · PYQ PAPER 2025

The largest interval, in which the function \(f(x)=x^3+2 x^2-1\) is increasing, is:

  1. A \((0, \infty)\)
  2. B \((-4,4)\)
  3. C \(\left[-\frac{4}{3}, 0\right]\)
  4. D \(\left(-\infty,-\frac{4}{3}\right] \cup[0, \infty)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\left(-\infty,-\frac{4}{3}\right] \cup[0, \infty)\)

Step-by-step Solution

Detailed explanation

\(f'(x) = 3x^2 + 4x\) \(3x^2 + 4x \ge 0 \Rightarrow x(3x+4) \ge 0\) \(x \in \left(-\infty, -\frac{4}{3}\right] \cup [0, \infty)\)