# Graphs of function g(x)

1. Nov 29, 2012

### salma17

Let g(x) be a function where g(0)=0, g(2)=0 and g'(4)=0. Which of the following is a possible graph of g(x)? (I have attached an image of the graphs) First, I immediately eliminated choice C) because g(0) isnt 0. I dont really get what that little apostrophe means in g'(4)=0. Is that like the derivative? If someone can please explain this to me, Id appreciate it. thanks!

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2. Nov 29, 2012

### micromass

Staff Emeritus
Yes, $g^\prime$ is the derivative of g.

3. Nov 29, 2012

### salma17

Can you please explain to me an easy way I can find the derivative of the graph?

4. Nov 29, 2012

### micromass

Staff Emeritus
What is the derivative? What is the geometrical interpretation of the derivative??

5. Nov 29, 2012

### symbolipoint

The original posting and replies belong in the Calculus & Beyond board section.

As for finding the choice of graph matching the required values, just look at each graph and compare with the required values. The easy part is checking which graphs have g(x)=0. You require g(0)=0 and g(2)=0. WHICH choices of graph fit this? WHICH choices of graph do NOT fit this? [STRIKE]You may find that the given information of the derivative is not necessary.[/STRIKE] Do you know what is a derivative?

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

### salma17

umm dy/dx?

7. Nov 29, 2012

### micromass

Staff Emeritus
Yes, but what does the derivative mean?? Why did we bother to introduce it?

8. Nov 29, 2012

### salma17

they're the values of the function..and its a limit?

9. Nov 29, 2012

### SammyS

Staff Emeritus
No, the derivative is not the value of a function.

Yes, it is a limit.

Another hint: The derivative gives the slope of something. What does it give the slope of?

10. Nov 29, 2012

### salma17

the tangent line? I dont get how I can find the slope of this graph if there are no numbers, and just letters?

11. Nov 29, 2012

### SammyS

Staff Emeritus
Not quite right.

The derivative gives you the slope of the tangent line.

For graph A: Is the slope of the line tangent to g(x) at x = 4 positive? ... or is it negative? ... or is it zero?

For graph B: Is the slope of the line tangent to g(x) at x = 4 positive? ... or is it negative? ... or is it zero?

...

12. Nov 29, 2012

### salma17

for graph A: its positive. because it goes up?
for B: negative
for C:positive
for D:zero
is this right?

13. Nov 29, 2012

### Staff: Mentor

Who is "it"? If you want to be understood, don't use "it", especially when you're talking about two different things (which I think you are).

14. Nov 29, 2012

### SammyS

Staff Emeritus
I assume you're answering my previous question which was:
You could eliminate some confusion by either answering more completely, for example:
for graph A: The slope of the tangent line at x = 4 is positive, because the graph of g(x) goes up? ...​

Alternatively, you could use the "QUOTE" feature to reply to my post. Then what you're referring to would be clearer, although your reply would still be somewhat ambiguous.

If your reply is referring to the slope of the tangent line at x = 4, then your responses are correct.

With those answers, can you successfully identify the correct graph from the Original Post in this thread?

15. Nov 29, 2012

### salma17

I'll go with B. final answer...

16. Nov 29, 2012

### Staff: Mentor

Nope

17. Nov 29, 2012

### salma17

I feel dumb. Please tell me its A

18. Nov 29, 2012

### SammyS

Staff Emeritus

Only one of the graphs has g'(4)=0 .

19. Nov 29, 2012

### salma17

ohhh..so its 0 when the graph doesnt go through point 4.which is D

20. Nov 29, 2012

### Staff: Mentor

Please give an answer that indicates what is being asked, without using "it". Also, there is no point 4.

When you say "it" I don't know what you're referring to, and I have to go back to post #1 to look at the graph.