  We consider radial solutions of the slightly subcritical problem $-\Delta
u_\varepsilon = |u_\varepsilon|^{\frac{4}{n-2}-\varepsilon}u_\varepsilon$
either on $\mathbb R^n$ ($n\geq 3$) or in a ball $B$ satisfying Dirichlet or
Neumann boundary conditions. In particular, we provide sharp rates and
constants describing the asymptotic behavior (as $\varepsilon\to 0$) of all
local minima and maxima of $u_\varepsilon$ as well as its derivative at roots.
Our proof is done by induction and uses energy estimates, blow-up/normalization
techniques, a radial pointwise Pohozaev identity, and some ODE arguments. As
corollaries, we complement a known asymptotic approximation of the Dirichlet
nodal solution in terms of a tower of bubbles and present a similar formula for
the Neumann problem.
