A Slope Ratio Maximum

Problem

The three lines

l_1:y=k_1x,\qquad l_2:y=k_2x+1,\qquad l_3:y=k_3(x-1)

bound a triangle of area $4$ , and $k_1<0<k_2<k_3$ . Find the maximum value of $\dfrac{k_2}{k_3}$ .

Answer

Solution

Difficulty	8/10
Topics	Extrema, AM-GM, analytic geometry

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