Explain: True or False: If $\frac{dx}{dy}=\frac{1}{dy/dx}=0$, then tangent line to the curve $y = f(x)$ is horizontal.
The answer is false. But I don't know why. Here's my train of thought and would love for someone to guide me:
- If (the inverse of) $\frac{1}{\Delta y/\Delta x} = 0$, then there must be a zero in the non-inverse derivative $\frac{\Delta y}{\Delta x}$.
- If this is true, that means there's a maximum or minimum value to the curve.
- Which means for the function, there'd be a part of the curve that will be $0$
However they never stated where the tangent line is drawn, so there's a possibility that it can be true?
Would like to understand this and it'd be great if you can me identify my knowledge gap?