The Convex(f, t, x(t)) command determines if the integrand is convex.

If the integrand is convex, the functional  is globally minimized by extremals (solutions of the Euler-Lagrange equations).

For a convex integrand, the output is an expression sequence containing two items:

Hessian matrix  

Logical expression that is true iff the Hessian is positive semidefinite, which proves that J is a minimum

If the integrand is not convex, Maple returns false.

If LinearAlgebra[IsDefinite] cannot determine the convexity, the output is an expression sequence containing two items:

Hessian matrix  

unevaluated call to IsDefinite

If an error occurs in the execution of LinearAlgebra[IsDefinite], only the Hessian matrix is returned.

The arithmetic negation makes the Hessian negative semidefinite.