= Parameter bounds on maximum lift-to-drag ratio
\b[Parameter bounds on maximum lift-to-drag ratio] describe how an allowed set of <drag polar> parameters limits the optimum predicted by that model. For the positive <parabolic drag polar>, write $c=C_{D0}>0$ and
$$
F(c,k)=(L/D)_{\max}=\frac1{2\sqrt{ck}},\qquad k>0.
$$
This is the unconstrained model optimum; an allowable range of <lift coefficients> can reduce the attainable value.
The derivatives $\partial F/\partial c=-F/(2c)$ and $\partial F/\partial k=-F/(2k)$ show that $F$ decreases with either parameter. Consequently, positive bounds $c\in[c_-,c_+]$ and $k\in[k_-,k_+]$ imply
$$
\boxed{\frac1{2\sqrt{c_+k_+}}\le F(c,k)\le\frac1{2\sqrt{c_-k_-}}.}
$$
This <interval arithmetic> argument is global over the rectangle, without a small-error approximation.
An original example uses $c\in[0.018,0.022]$ and $k\in[0.045,0.055]$. The predicted optimum ratio lies between about 14.374 and 17.568. Its optimizing lift coefficient lies in the different interval
$$
\sqrt{c_-/k_+}\le C_L^{\rm opt}\le\sqrt{c_+/k_-},
$$
or approximately $[0.5721,0.6992]$. A range of performance values and a range of operating points answer different questions.
A rectangular enclosure can be conservative. For a separate joint-parameter example, suppose fitting constrains $k=0.001/c$ exactly over a positive interval of $c$. Then the product $ck$ is constant and every allowed pair gives $F=15.8114$, even though each parameter varies. Combining independent marginal extremes would include pairs excluded by that relation.
For small random parameter errors, first-order propagation instead gives
$$
\frac{u_F^2}{F^2}\simeq\frac14\left[\frac{u_c^2}{c^2}+\frac{u_k^2}{k^2}
+\frac{2\operatorname{cov}(c,k)}{ck}\right].
$$
The <covariance> term is needed when parameters are correlated, consistent with the primary metrological propagation law.<Guide to the expression of uncertainty in measurement by JCGM>[Section 5.2.2, equation 13, correlated input quantities]{ref} A standard uncertainty is not automatically a hard interval bound. Neither calculation includes failure of the assumed polar outside its fitted regime, and neither by itself identifies one operating point that is optimal for every parameter pair.
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