To find: The points at which the slope of the curve is -1.
The slope of the curve is -1 at the points .
The curve .
Differentiate implicitly with respect to x,
Apply the product rule,
Apply the chain rule and simplify the terms,
Thus, the derivative of the equation is .
That is, the slope of the tangent is .
Obtain the required points such that the slope of the tangent is -1.
Simplify the expression,
Substitute in the left hand side of the equation ,
That is, .
Therefore, the equation has no solution when .
Substitute in the curve equation ,
Thus, the real solution are and .
Substitute in , the points are
Therefore, the slope of the curve is -1 at the point .
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