Show, with clear working and explanation, why the curve $y=\frac{4-6x}{1-2x}$ has no turning point

Question

Show, with clear working and explanation, why the curve $y=\frac{4-6x}{1-2x}$ has no turning point.

Accepted Answer

No turning point because $\frac{\mathrm dy}{\mathrm dx}=\frac2{(1-2x)^2}>0$ for $x\ne\frac12$

Differentiation - Applications of Differentiation — General