Locate the critical points of the following function. Then use the Second Derivative Test to determine whether they correspond to local maxima, local minima, or neither.
f(x) = 2x^2 e^-2x
What is(are) the critical point(s) of f? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The critical point(s) is(are) x = . (Use a comma to separate answers as needed.)
B. There are no critical points for f.
What is(are) the local minimum/minima of f? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The local minimum/minima of f is/are at x = .
(Use a comma to separate answers as needed.)
B. There is no local minimum of f.
What is(are) the local maximum/maxima of f? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The local maximum/maxima of f is/are at x = .
(Use a comma to separate answers as needed.)
B. There is no local maximum of f.