1. Nov 29, 2012

### salma17

Im working on my study guide..and I have no idea how to do these types of problems.Can anyone please just give me a hint on how I can approach these?
I attached the graph.

a few of the questions im having trouble with are:

At which point is f(x) > 0?
a) A b) B c) C d) D e) None of these

At which point is f'(x)> 0?
a) A b) B c) C d) D e) None of these

At which point is f'(x) =0 ?
a) A b) B c) C d) D e) None of these

Id appreciate any feedback I get. thanks
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

#### Attached Files:

• ###### graph2.png
File size:
19.9 KB
Views:
85
2. Nov 29, 2012

### HallsofIvy

Staff Emeritus
For (a), you look at the graph! Or are you saying that you do not know what "f(x)> 0" means?

For (b) and (c), you have to know what f' means. It is the "slope of the tangent line". As long as the graph is increasing, f' is positive. As long as the graph is decreasing, f' is negative.

3. Nov 29, 2012

### salma17

Yea, I dont know what it means. I learned all this material last year, and it was really easy to me back then, and now I have to know it for my next math class, and I forgot everything :/ So for a), its basically asking which point in the Y-axis is greater then 0? Which are letters A and H, right?

4. Nov 29, 2012

### salma17

5. Nov 29, 2012

### skiller

What?
Are you sure you've quoted the question correctly? Your multiple choice answers only include points A, B, C and D, but your attached graph also has points E, F, G and H.

6. Nov 29, 2012

### salma17

Yes, thats how it is on my study guide. So im thinking if any of the answer ends up to be either E,F,G or H, then it will be "none of these".

7. Nov 29, 2012

### skiller

If the options are A, B, C, D or None of these, and you think the possible correct answers are A and H, then why would you say "None of these"?

8. Nov 29, 2012

### salma17

Im not saying that. above I said the answers for part a) should be A and H. in my previous post,im saying if an answer(in general) is either E,F,G,or H, then it will be none of these.
Anyways, am I right about part A?

9. Nov 29, 2012

### skiller

You haven't labelled any question as "Part A" etc, but yes you are correct for the first one.

For the others, do you understand what f'(x) means, as HallsofIvy asked? (He did actually explain what it meant, too.)

Last edited: Nov 29, 2012
10. Nov 29, 2012

### salma17

ok so for the question At which point is f'(x)> 0? , I look at the graph to see which point above 0 the graph is increasing at? which is at letter H, correct?

Last edited: Nov 29, 2012
11. Nov 29, 2012

### haruspex

Why would you only consider points above 0?

12. Nov 29, 2012

### salma17

because the first part its asking what y-coordinate is greater than 0? or am i totally wrong?

13. Nov 29, 2012

### haruspex

That was the first part, this is the second part.

14. Nov 29, 2012

### salma17

because it says >0 so greater then 0? I honestly have no idea how to even begin this one

15. Nov 29, 2012

### haruspex

The first part asked for f() > 0. That is, the function > 0.
The second part asks for f'() > 0. That is, the gradient greater than zero. That is independent of whether the function, f, is greater than zero. So it can be anywhere on the graph as long as it slopes from lower left to upper right.

16. Nov 29, 2012

### salma17

ohh so I have to look at where the slope is increasing..so its from point F to H

17. Nov 29, 2012

### Staff: Mentor

No, where the slope is positive. This is exactly the same as where f'(x) > 0.

This is not the same as "where the slope is increasing." None of the questions asked where the slope was increasing.

18. Nov 29, 2012

### salma17

I drew the tangents on each point, and I got positive slopes at points C,D,E and H. If this wrong, then Im drawing my tangents wrong and I'll need to youtube how to drank tangents.

19. Nov 29, 2012

### haruspex

Distinguish clearly in your mind the following:
- the places where f() > 0; that is the portion above the x axis.
- the places where f'() > 0; f'(x) is the slope at x. Where the slope > 0, f is increasing as x increases. The graph slopes from lower left to upper right. That can be a positive f getting larger, or a negative f getting less negative (or becoming positive).
- the places where f''() > 0; these sections are where the slope is increasing. Viewed from below the curve, the curve is convex. That can be a positive slope getting steeper, or a negative slope getting shallower (or becoming positive).
All 8 combinations (f being +/-, f' being +/-, f'' being +/-) can occur.

20. Nov 29, 2012

### Staff: Mentor

The slopes of the tangent lines at D and H are positive, yes.

Pretty clearly, the slopes of the tangent lines at C and E are NOT positive. Why do you think they are?