Each of the functions in Exercises 40–45 has a critical point at the origin. For eac...

Each of the functions in Exercises 40–45 has a critical point at the origin. For each function, (a) check that the Hessian fails to provide any information about the nature of the critical point at the origin, and (b) find another way to determine if the function has a maximum, minimum, or neither at the origin.