E Computation of the K-functions in Chapter 7

Note that both the supremums in (E.1) and (E.2) can be attained only possibly at a, b and the stationary points of the function

gh(x) = x˜′t√ x˜′Δx˜

.

Now dgh(x)

dx =

(( dx˜′

dx

) t(x˜′Δx˜)− (x˜′t)

( dx˜′

dx

) Δx˜

) (x˜′Δx˜)−3/2.