Find the absolute and local maximum and minimum values of f

[Vala]

Hi. I am having some problems with finding the absolute and local extremes. Could anyone help me with these problems?

Directions:
Find the absolute and local maximum and minimum values of f

Problems:
1. f(x) = 8 - 3x, x >= 1
f'(x) = -3 -- This is as far as I get. I don't know what to do now.

2. f(x) = x^2, 0 < x < 2
f'(x) = 2x -- Same thing here. I can get the derivative, but I don't know the next steps to find both the absolute and local max/min.

 

[tkhunny]

Question #1 - Is the derivative ever zero (0)?

Is -3 ever 0? I think not.

Question #2 - Is there anything the derivative doesn't know about? That would be end points, corners, various discontinuities.

In the case of f(x) = 8 -3x, the answer is NO!
In the case of f(x) = 8 - 3x for x >= 1, you had better investigate around x = 1.