Ok I am not going to solve this problem for you, but I'll do my best to point you in the right direction so you can solve it yourself. Forgive me if I miss something or completely butcher it... my calc skills are way past their "sell by" date
Lets start with the obvious, and you can put 2 and 2 together
a)
-Relative extrema just means relative maximum or minimum. One of these two extrema will occur when the rate of change goes from positive to negative or vice-versa.
-In order for that to happen, the rate of change must hit zero.
-The first derivative is the rate of change. Solve for 0.
-Once you find such points, you need to make sure whether each is a maximum or a minimum.
b)
- Points of Inflection are points where the curve changes from curving up to curving down, or vice-versa.
- This means somewhere between curving up and curving down, the function is NOT curving anywhere, ie: the rate of change is 0.
- Rate of change is the first derivative. Solve for 0.
Good luck
PS: Critical point = min, max, or inflection point.
PPS: I DID butcher it! Fixed now.. I hope.