csat-suneung 2017 Q15

csat-suneung · South-Korea · csat__math-science 4 marks Applied differentiation Tangent line computation and geometric consequences

Let P be a point on the curve $y = 2 e ^ { - x }$ at $\mathrm { P } \left( t , 2 e ^ { - t } \right)$ $(t > 0)$. Let A be the foot of the perpendicular from P to the $y$-axis, and let B be the point where the tangent line at P intersects the $y$-axis. What is the value of $t$ that maximizes the area of triangle APB? [4 points]
(1) 1
(2) $\frac { e } { 2 }$
(3) $\sqrt { 2 }$
(4) 2
(5) $e$

Let P be a point on the curve $y = 2 e ^ { - x }$ at $\mathrm { P } \left( t , 2 e ^ { - t } \right)$ $(t > 0)$. Let A be the foot of the perpendicular from P to the $y$-axis, and let B be the point where the tangent line at P intersects the $y$-axis. What is the value of $t$ that maximizes the area of triangle APB? [4 points]\\
(1) 1\\
(2) $\frac { e } { 2 }$\\
(3) $\sqrt { 2 }$\\
(4) 2\\
(5) $e$

Paper Questions

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