Cases where Simpson's rule has a greater error than Trapezoidal rule?

The error bound formulas for trapezoidal rule and simpson's rule say that:

$\begin{array}{l}{\text { Error Bound for the Trapezoid Rule: Suppose that }\left|f^{\prime \prime}(x)\right| \leq k \text { for some } k \in \mathbb{R} \text { where }} \\ {a \leq x \leq b . \text { Then }} \\ {\qquad\left|E_{T}\right| \leq k \frac{(b-a)^{3}}{12 n^{2}}} \\ {\text { Error Bound for Simpson's Rule: Suppose that }\left|f^{(4)}(x)\right| \leq k \text { for some } k \in \mathbb{R} \text { where }} \\ {a \leq x \leq b . \text { Then }} \\ {\qquad\left|E_{S}\right| \leq k \frac{(b-a)^{5}}{180 n^{4}}}\end{array}$

Using these formulas, is it possible to find functions where Trapezoid Rule is more accurate than Simpson's rule? Maybe starting off with something like:

$k_T \frac{(b-a)^{3}}{12 n^{2}} \leq k_S \frac{(b-a)^{5}}{180 n^{4}}$

$k_T {15 n^{2}} \leq k_S {(b-a)^{2}}$

If we cant use this inequality. How can I identify functions where Trapezoidal rule is more accurate than Simpson's rule.