for the derivative is
following that logic, derivative of is and
for the derivative is given as
so for the derivative is and the double derivative is
find the inflection points by setting F''(x) to zero and solving for x.
check where it is positive and where it is negative i.e. find concavity
you should end up with one concave down which means there is only one maximum.
how many concave up you end up isn't important here.