The contours of a function $f$ are shown in the figure below.

For each of the points shown, indicate whether you think it is a local maximum, local minimum, saddle point, or none of these.

(a) Point P is ? a local maximum a local minimum a saddle point none of these

(b) Point Q is ? a local maximum a local minimum a saddle point none of these

(c) Point R is ? a local maximum a local minimum a saddle point none of these

(d) Point S is ? a local maximum a local minimum a saddle point none of these