Math Problem Statement

Find the maximum area of a triangle formed in the first quadrant by the -axis, -axis and a tangent line to the graph of .

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Optimization
Geometry

Formulas

Equation of tangent line: y - e^{-x_0} = -e^{-x_0}(x - x_0)
Area of a triangle: A = (1/2) × base × height
Optimization formula for area: A = (1/2) × e^{-x_0} × (x_0 + 1)^2

Theorems

Maximization of functions using derivatives

Suitable Grade Level

Undergraduate Calculus