Introduce lagrange multipliers for each of the two

Question

Maximum entropy:-

Solve problem by the following steps:

(a) Introduce Lagrange multipliers for each of the two constraints, and differentiate the resulting Lagrangian integral with respect to p at each point x. Set this derivative to zero.

(b) Show that ln p(x) = c - dx² for some constants c and d.

(c) Evaluate the constants to satisfy the two constraints.