= Solution
An attached similarity profile must approach $f'\to A$ as $\eta\to\infty$. Linearizing about $f\sim A\eta+\text{constant}$ gives, for the small <velocity> correction $g=f'-A$,
$$
g''+\frac{\alpha A}{2}\eta g'-2\alpha A g\simeq0.
$$
When $\alpha A>0$, one independent far-field correction decays with a Gaussian factor; when $\alpha A<0$, the two nontrivial asymptotic modes grow, one algebraically and one exponentially, so a nonconstant wall profile cannot decay into the prescribed outer flow. Thus the attached exponential similarity construction requires
$$
\boxed{\alpha A>0.}
$$
Equivalently the outer speed increases along the direction of motion, giving a favorable <pressure gradient>. In the intended flow away from the leading edge along positive $x$, this means \b[$A>0$ and $\alpha>0$]. The sign-reversed choice $A<0,\alpha<0$ describes locally favorable flow in the opposite direction; it is not a layer developing downstream from the stated leading edge.
The asymptotic approximation also requires a geometrically thin layer, away from the leading-edge region. Comparing its thickness with the streamwise variation length $1/|\alpha|$ gives the local condition $\mathrm{Re}|A|e^{\alpha x}/|\alpha|\gg1$. An exponentially decaying outer speed eventually violates this condition on an infinite downstream interval. These scale and orientation requirements distinguish formal similarity reduction from a uniformly valid attached <boundary layer>.
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