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The normal to the curve y(x − 2)(x − 3) = x + 6 at the point where the curve intersects the y-axis passes through the point:
- (1/2, 1/2)
- (1/2, −1/3)
- (1/2, 1/3)
- (−1/2, −1/2)
Correct answer: (1/2, 1/2)
Solution
The normal to the curve at the y-axis intersection point has a slope that is the negative reciprocal of the tangent slope at that point. After calculating the slope of the tangent and the equation of the normal line, it can be verified that the point (1/2, 1/2) lies on this normal line, confirming it as the correct answer.
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