JEE Advanced · Mathematics · 25. AOD
Paragraph:
Consider the polynomial \(f(x)=1+2 x+3 x^2+4 x^3\). Let \(s\) be the sum of all distinct real roots of \(f(x)\) and let \(t=|s|\).Question:
The function \(f^{\prime}(x)\) is
- A
increasing in \(\left(-t,-\frac{1}{4}\right)\) and decreasing in \(\left(-\frac{1}{4}, t\right)\)
- B
decreasing in \(\left(-t,-\frac{1}{4}\right)\) and increasing in \(\left(-\frac{1}{4}, t\right)\)
- C
increasing in \((-t, t)\)
- D
decreasing in \((-t, t)\)
Answer & Solution
Correct Answer
(B)
decreasing in \(\left(-t,-\frac{1}{4}\right)\) and increasing in \(\left(-\frac{1}{4}, t\right)\)
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