# Increasing function

1. Jan 25, 2010

### songoku

1. The problem statement, all variables and given/known data
The largest interval on which the function f(x) = x2 + 4x + 2 is increasing is

a. [0, ~)
b. (-~, 0]
c. [-2, ~)
d. (-~, -2]
e. (-2, ~)

2. Relevant equations
differentiation

3. The attempt at a solution
I am not sure the answer is (c) or (e). The condition that the function is increasing is f '(x) > 0 or f ' (x) $$\geq$$ 0?

Thanks

2. Jan 25, 2010

### tiny-tim

Hi songoku!

(have an infinity: ∞ and a geq: ≥ )
"increasing" means > 0; ''non-decreasing" would be ≥ 0.

3. Jan 25, 2010

### songoku

Hi tiny-tim

Thanks a lot !!! (again)

4. Jan 25, 2010

### Staff: Mentor

But there's also the distinction between "increasing" - f'(x) >= 0 and "strictly increasing" - f'(x) > 0. And similar for decreasing vs. strictly decreasing.

5. Jan 25, 2010

### songoku

Hi Mark

Hm...so what is the appropriate condition used for this question? Thanks

6. Jan 25, 2010

### Staff: Mentor

Well, I would go with c) - [-2, inf)

7. Jan 30, 2010

### songoku

Hm...I think I'm with you Mark

8. Jan 31, 2010

### HallsofIvy

Songoku, the difficulty is that some textbooks use the "increasing", "nondecreasing" terminology while others use "increasing", "strictly increasing".

You ought to check with our teacher or your textbook to make sure which your class is using.

9. Jan 31, 2010

### songoku

Hi HallsofIvy

Ok, I'll do it. Thanks a lot for your suggestion