Both Extremes Inside

★ 6/10Quadratic Equations Extrema calculus AM-GM Vieta's Formulas

Problem

The function

f(x) = \frac13 x^3 + \frac12 b x^2 + cx + d

has both a local maximum and a local minimum in the interval $(0, 1)$ . Find the range of

c^2 + (1+b)c.

Answer

Solution

Difficulty	6/10
Topics	Quadratic Equations, Extrema, calculus, AM-GM, Vieta's Formulas

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