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Consider the polynomial$$f(x) = 1 + 2x + 3x^2 + 4x^3$$.Let s be the sum of all distinct real roots of f(x) and let $$t = \mid s \mid$$.
The function $$f'(x)$$ is
increasing in $$\left(-t, -\frac{1}{4}\right)$$ and decreasing in $$\left(-\frac{1}{4}, t\right)$$
decreasing in $$\left(-t, -\frac{1}{4}\right)$$ and increasing in $$\left(-\frac{1}{4}, t\right)$$
increasing in (-t, t)
decreasing in (-t, t)
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