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The area of the region enclosed by the x-axis, the tangent, and the normal drawn to the curve 4x³ - 3xy² + 6x² - 5xy - 8y² + 9x + 14 = 0 at the point (-2, 3) is A. Find 8A.

1. 1
2. 2
3. 4
4. 8

Correct answer: 2

Solution

Differentiating implicitly and evaluating at (-2,3) gives the slope of the tangent. The tangent and normal intersect the x-axis at two points. The region bounded by tangent, normal, and x-axis is a triangle. Using coordinate geometry find the area, then compute 8A.

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