What Does g'(4)=0 Indicate About the Graph of Function g(x)?

[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) isn't 0. I don't 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!

 

[micromass]

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

 

[salma17]

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

 

[micromass]

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

 

[symbolipoint]

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) isn't 0. I don't 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!

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?

 

[salma17]

umm dy/dx?

 

[micromass]

umm dy/dx?

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

 

[salma17]

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

 

[SammyS]

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

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?

 

[salma17]

the tangent line? I don't get how I can find the slope of this graph if there are no numbers, and just letters?

 

[SammyS]

the tangent line? I don't get how I can find the slope of this graph if there are no numbers, and just letters?

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?

...

 

[salma17]

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

 

[Mark44]

for graph A: its positive. because it goes up?

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).

for B: negative
for C:positive
for D:zero
is this right?

 

[SammyS]

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

I assume you're answering my previous question which was:

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?

...

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?

 

[salma17]

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

 

[Mark44]

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

Nope

 

[salma17]

I feel dumb. Please tell me its A

 

[SammyS]

Let g(x) be a function where g(0)=0, g(2)=0 and g'(4)=0.
...

I feel dumb. Please tell me its A

Look at your answers for the slope at x=4.


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

 

[salma17]

ohhh..so its 0 when the graph doesn't go through point 4.which is D

 

[Mark44]

ohhh..so its 0 when the graph doesn't go through point 4.which is D

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.

 

[symbolipoint]

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) isn't 0. I don't 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!

Examine the parts of this equation, g'(4)=0, and decide which of the choices A, B, C, D, match this equation. You know that g' is a derivative. What is the value for x in this derivative? What does g'(4)=0 mean? What does it look like? Which graph shows this?