does y=1/x and y=x^3 ever have the same slope? if so, where?

2 answers

No, y=1/x and y=x^3 never have the same slope. The slope of y=1/x is -1/x^2, and the slope of y=x^3 is 3x^2. Since these two equations have different slopes, they can never have the same slope.
while the answer is ultimately correct, the logic is unsound.
Suffice it to say that -1/x^2 is always negative
and 3x^2 is never negative, so there is nowhere that they can be equal.