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For the curve y = e^(- |x|), determine the point P(x, y) at which the tangent line, together with the two coordinate axes, encloses the maximum possible area.
- (1, 1/e)
- (1, -1/e)
- (e, 1/e)
- (-1, e)
Correct answer: (1, 1/e)
Solution
The point (1, 1/e) is correct because at this point, the slope of the tangent line maximizes the area enclosed with the axes, resulting in the largest possible area under the curve.
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