Letfbe the function defined by

f(x) =xⁿ(x+ 3),wherenis an integer that is greater than or equal to2.

(a) Find all critical points off.

(b) Find the the intervals on whichfis increasing or decreasing,

(c) Use the information from the previous two parts to fifind determine whether the critical points are local maxima, local minima, or neither. (Do not use any information about the second derivative; just the sign of the fifirst derivative.)

Note: You may not assume thatnis any particular integer. Your answers to some of the parts above will be different for differentn's. For example, you may fifind different behaviours whennis even or whennis odd.