Help in College Level Calculus

Here is the problem that is on my final review that I'm currently having trouble with:

Find the maximum and minimum values, if they exist over the indicated interval:
a) f(x)= 3x-8; [-2,1]

b) f(x)= x^3-4x^2+5x+9; [-2,3]

I know that I should find critical numbers by finding the first derivative and setting it zero and solving. Using those critical points, I test on a number line using test points that fall between the intervals of the critical numbers. I then plug those test points into the derivative to see if it is increasing/decreasing, thus finding where the function is at a max or min.

These are giving me problems because when I graph,for example letter a, I get a straight line with no visible mins or max.

Here are the answers as stated in the answer guide for this problem if anyone needs them to reference:
a) minimum (-2,-14), maximum (1,-5)
b) Rel. Max (1,11), Rel Min (5/3, 293/27), Abs. Max (3,15), Abs. Min (-2,-25)

The directions for all the problems stated say to find the max and min values, not mentioning anything about the Absolutes. So how do I know when to find just the relative min/max, the absolute mins/max or both?

Thanks for the help...

your confusion is based around the idea that the problem is asking for any local/absolute max/min. It isn't. It is simply asking for the max and min over a given interval.

Your first method is correct to find any local max or min values inside this interval. However, you must then test the function at the endpoints to determine if these are higher or lower than the values at the critical points.

For a, as you already correctly determined, there is no local max or min values inside the interval because it has no critical points. This is the first part of the problem. Now you must test

f(a) and f(b) where the interval is [a, b]. In this case the interval is [-2, 1]. Plugging in the endpoints of this interval gives