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CUET · MATHS · PYQ PAPER 2025

The largest open interval in which the function \(f(x)=4 x^3-5 x^2-8 x+12\) increases, is:

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

Answer & Solution

Correct Answer

(B) \(\left(-\infty, -\frac{1}{2}\right) \cup\left(\frac{4}{3}, \infty\right)\)

Step-by-step Solution

Detailed explanation

\(f'(x) = 12x^2 - 10x - 8\) \(12x^2 - 10x - 8 = 0\) \(6x^2 - 5x - 4 = 0\) \(x = \frac{5 \pm \sqrt{(-5)^2 - 4(6)(-4)}}{2(6)}\) \(x = \frac{5 \pm \sqrt{25 + 96}}{12}\) \(x = \frac{5 \pm 11}{12}\) \(x = -\frac{1}{2}, \frac{4}{3}\)…