An Interval That Fits Itself

★ 4/10functions Extrema Monotonicity algebra Casework

Problem

The function $f(x) = -\dfrac{1}{2}x^2 + \dfrac{13}{2}$ , restricted to an interval $[a, b]$ , has minimum value $2a$ and maximum value $2b$ . Find the interval $[a, b]$ .

Answer

Solution

Difficulty	4/10
Topics	functions, Extrema, Monotonicity, algebra, Casework

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