Given the equation $$\frac{d^ky}{dx^k}=c$$ where $k$ represents the number of higher-order derivatives and $c$ represents any constant real number except $0$.
Eg : $$\frac{d^{11}y}{dx^{11}}=100$$ Can I conclude that the curve of the function has no inflection points?
The general solutions are the polynomial of degree $k$ with leading term $\frac{c}{k!}x^k$. These polynomial can have an inflection point, but they don’t need to. There are polynomials with no inflection point and there are polynomials with inflections points.
The polynomial $p$ must have an inflection point, if it is of odd order, since then $p’’$ is a polynomial of odd degree (or the polynomial $0$), which must have a root over $\mathbb{R}$.