Final answer:
The slope of the curve 7xy = 5 at the point (1, 5/7) is -5/7.
Step-by-step explanation:
To find the slope of the curve given by the equation 7xy = 5 at the point (1, 5/7), we can take the derivative of the equation with respect to x and then evaluate it at x = 1. Differentiating both sides of the equation gives us: 7y + 7xy' = 0. To find y', we can solve this equation for y'.
From the given equation, we have 7xy = 5. Differentiating both sides with respect to x gives 7y + 7xy' = 0. Rearranging this equation, we get y' = -y/x. Substituting x = 1 and y = 5/7, we can find the slope at the point (1, 5/7).
Therefore, the slope of the curve 7xy = 5 at the point (1, 5/7) is -5/7.