Increasing Function Homework: Largest Interval

[songoku]

Homework Statement

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, ~)

Homework Equations

differentiation

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

 

[tiny-tim]

Hi songoku!

(have an infinity: ∞ and a geq: ≥ )

… The condition that the function is increasing is f '(x) > 0 or f ' (x) \geq 0?

"increasing" means > 0; ''non-decreasing" would be ≥ 0.

 

[songoku]

Hi tiny-tim

Thanks a lot ! (again)

 

[Mark44]

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

 

[songoku]

Hi Mark

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

 

[Mark44]

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

 

[songoku]

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

 

[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.

 

[songoku]

Hi HallsofIvy

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