= Solution
Assume the denominators are defined, so $c,d\ne0$. For a <descent direction> $p$, set $\varphi(\alpha)=f(x+\alpha p)$. The <Wolfe conditions> are
$$
\varphi(\alpha)\leq\varphi(0)+\sigma\alpha\varphi'(0),\qquad
\varphi'(\alpha)\geq\eta\varphi'(0),\qquad0<\sigma<\eta<1.
$$
The first is sufficient decrease and the second is the curvature condition. Here
$$
H=\nabla^2 f=
\begin{pmatrix}c^{-2}+d^{-2}&c^{-2}-d^{-2}\\c^{-2}-d^{-2}&c^{-2}+d^{-2}\end{pmatrix}
$$
is positive definite, with <eigenvalues> $2/c^2,2/d^2$. The exact step is
$$
\alpha_*=-\frac{\nabla f(x)^Tp}{p^THp}>0.
$$
It gives $\varphi'(\alpha_*)=0$, so the curvature condition holds. Its decrease is $\varphi(\alpha_*)-\varphi(0)=\alpha_*\varphi'(0)/2$, so sufficient decrease holds for the usual choice $0<\sigma\leq1/2$, $\sigma<\eta<1$. Hence \b[exact searches satisfy Wolfe with an Armijo constant at most one half]. If one allowed $\sigma>1/2$, even an exact quadratic minimizer would fail that condition; the parameter range matters.
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