Power Functions

[kendang]

I'm learning the first unit of Advanced Functions and I'm already stuck. I would really appreciate some help especially on these questions:

Consider the function f(x) = -2(x+1)^2(x+2)^2

1. What number of difference yields the finite difference for f(x)?

a) 2nd
b) 3rd
c) 4th
d) 5th
e) none

I tried to sub x into the equation eg. f(0) to f(5) and see which when I subtract the differences will be the same... but I couldn't find the row which gave me the same difference.

2. Common finite difference for f(x)?

a) -2
b) -24
c) -3
d) -48
e) none

This is the the common difference... which I couldn't get.

3. How many turning points of f(x)?

a) 2
b) 4
c) 3
d) 1
e) none

I choose "d) 1" because the highest power is "2" and the number of turning points is the "power-1".

4. f(x), which is NOT true?

a)two x-int
b) two double roots
c) one of its zero is less than zero
d) it has only real roots
e) none, it has all

I have no idea?

 

[tkhunny]

I'm not convinced we have a good definition of "finite difference". It looks like it may be intended to mean "constant difference". Really, tell me why the first differences are NOT "finite".

Most have to do with the degree of the entire expression. Some, just parts of it.

These are eyeball problems. You should not be struggling with this.

1. Degree is 4, the first constant difference is the 4th. Done.
2. Degree is 4 and leading coefficient is -2, thus -2 * (4!). Done.
3. Degree is 4, so 4-1 = 3. Done.
4. You go ahead and discuss the last ones. You had better get an idea or you will not pass this class.