This exercise determines when certain plane curves are nonsingular.
a) Show that for any polynomial f(x)∈Z[x] and for any integer n≥2, the curve
C:yⁿ =f(x)
in R² has a singular point if and only if f(x) has a repeated root in R, i.e., there exists x₀ ∈ R with f(x₀)=0 and f'(x₀)=0.