What is the difference between rel. min and abs. min
ex) -x^4-2x^3+3x^2+3x+4
i have no clue how to find the rel max and min
or the abs max and min!!!
are there any min values?
I presume what relative min means is local min. As the function goes to -inf when x goes to +- inf, there is no absolute min. However if you plot it you'll probably see it goes up, then down, then up again, then down so it's a sort of M shape. The bottom of the middle bit is your local (relative) min.
The only way to do this without using calculus is to work out roughly where the min is by plotting it or whatever, and then seeing what happens either side of where you think the minimum is (you'll probably find there's a x^2 term in there which will be zero and therefore either side of it it goes + so making the function go uphill. Or something.
Okay, so the graph is like I said (probably) a sort of M shape. When you've worked out where the maxima (2 of them) and minimum is (1 of them) that's where it stops going up ("increasing") and starts going down ("decreasing").
Imagine you're travelling from far over to the left (where x is very negative), to way over to the right (where x is well positive) and look what f(x) is doing.
As you travel, the line you're on goes up, reaches a (local) maximum, then goes down, and reaches a (local) minimum, goes up again till it reaches another (local) maximum, then goes down again and falls off the bottom of the graph as it goes downwards forever.
The "intervals" it's asking for is the ranges of x where it's going up (for the "intervals where f(x) is increasing") and the ranges of x where it's going down.
The "increasing" intervals will be: the values of x between -infinity to where f(x) is at the first local maximum, and the values of x between where f(x) is at the local minimum to where it's at the second local maximum. It's decreasing everywhere else.