theorem hasDerivAt_valueFunction {J ρ c : ℝ} (hJ : 0 < J) :
HasDerivAt (fun x => valueFunction x ρ c) (valueFunctionDeriv J ρ c) J := by
simp only [valueFunction, valueFunctionDeriv]
exact (hasDerivAt_curvatureK_real (ne_of_gt hJ)).mul (hasDerivAt_perCapitaBenefit hJ)Paper 1c: Formal Calculus on K(J) and V(J)