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(a) what are the D-admissible directions for J?

(b) Find all possible (local) external points for J on D?

so far i have:

(let e be epsilon)

lim e->0 J(y+ev) - J(y) / e

= lim e->0 integ (a to b) [ sin^3(x) + (y+ev)^2(x)dx - J(y) ] / e

= lim e->0 integ (a to b) [2ey(x)v(x) + e^2v(x)^2) dx ] / e

= 2 integ(a to b) y(x)v(x) dx

A similar example was done in class, so i just copied it for this question.

G(y) = integ(a to b) y(x) dx = 1

gateaux G(y;v) = integ (a to b) y(x)v(x) dx

is this right so far? how do i go about answering (a) and (b).