A Shared Point Forces a Minimum

★ 8/10Extrema Substitution Monotonicity algebra inequality

Problem

Let $a,b\in\mathbb R$ with $a\neq 0$ . The curves

y=\frac{a+2}{x}\qquad\text{and}\qquad y=ax+2b+1

have at least one common point with $x$ -coordinate in the interval $[3,4]$ . Find the minimum value of $a^2+b^2$ .

Answer

Solution

Difficulty	8/10
Topics	Extrema, Substitution, Monotonicity, algebra, inequality

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