Answer:
True
Step-by-step explanation:
The integral

in the integral we have a product of a monomial: 
and an exponential function: 
In general case, when we have a combination of these two things you can use the integration by parts, where
will be
and
will be
.
The statement is true
Answer: terminating
Step-by-step explanation:
Compute the gradient of
.

Set this equal to the zero vector and solve for the critical points.








The last case has no real solution, so we can ignore it.
Now,


so we have two critical points (0, 0) and (2, 2).
Compute the Hessian matrix (i.e. Jacobian of the gradient).

Check the sign of the determinant of the Hessian at each of the critical points.

which indicates a saddle point at (0, 0);

We also have
, which together indicate a local minimum at (2, 2).