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A particle moves along the curve 6y = x...

A particle moves along the curve `6y = x^(3)+2`. Find the points on the curve at which the y-coordinate is changing 8 times as fast as the x-coordinate

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To solve the problem, we need to find the points on the curve defined by the equation \(6y = x^3 + 2\) where the y-coordinate is changing 8 times as fast as the x-coordinate. This means we need to find where \(\frac{dy}{dx} = 8\). ### Step-by-Step Solution: 1. **Understand the relationship**: We know that if the y-coordinate is changing 8 times as fast as the x-coordinate, we can express this mathematically as: \[ \frac{dy}{dx} = 8 \] ...
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