One Zero Only

★ 7/10functions Extrema calculus Monotonicity Discriminant

Problem

Let $f(x) = \dfrac13 x^3 - a\left(x^2 + x + 1\right)$ .

1. For $a = 3$ , find the intervals of monotonicity of $f$ . 2. Prove that $f$ has exactly one real zero (for every real $a$ ).

Answer

Solution

Difficulty	7/10
Topics	functions, Extrema, calculus, Monotonicity, Discriminant

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