CALLING OUT ALL CALCULUS BUFFS!!

[churchdoesmatter]

lim g(3) - g(x)
x->3 ------------- = -0.628 , then at the point x =3 , the graph of g(x)
............. 3 - x

A) is decreasing
B) is increasing
C) is concave upwards
D) is concave downwards
E) attains a relative minimum point

i really need help on this, this is mind-boggling, thanks

EDIT .. for the first part of the equation.. its g(3) - g(x) DIVIDED BY 3 - x ...

 

[churchdoesmatter]

^^

 

[Passions]

E

 

[churchdoesmatter]

BOBBY: how do you know its E?? any explaination or support fo ryour answer?

 

[churchdoesmatter]

aww

 

[Ns1]

n/m me stupid la

 

[amdskip]

I'm confused about what this problem is

 

[churchdoesmatter]

its like definition of a derivative

 

[erikiksaz]

Umm, i have no clue about that equation, it looks strange to me. Normally, to find the Increasing/Decreasing, you use the first derivative test. And to find concave up/down, you use the second derivative test. Hopefully you already know about those two.

 

[Daktaklakpak]

this is the definition of a derivative. since the derivative is negative, your function is decreasing.

A

 

[Ns1]

^^


rofl i can't believe i missed that

he's right y'know

 

[churchdoesmatter]

what about that at a point x=3 crap?

 

[Daktaklakpak]

the derivative is evaluated at the point x=3. that's what it means.

 

[Noriaki]

what do you mean by "the graph of g(x)
............. 3 - x"

?

Are we graphing g(x)? 3-x? g(3-x)? g(x)/(3-x)?
I'm not sure what we are graphing.

Also, maybe I'm missing something, but g(3) - g(3) would have to be 0, otherwise g isn't a function.
But lets say g(3) - g(3 - dx) = -0.628 (ie x is approaching 3, but not quite there, hence the -dx)

Therefore: g(3) - g(3 - dx) < 0, then: g(3) < g(3 - dx), thus g is decreasing. If I'm interpreting the information right then I'd say that A is the only one we can assume from this.

But I'm not even 50% sure I'm interpreting the question right.

(Oh, if it wasn't obvious, "dx" is some small number (according to standard calculus notation I should have used delta-x not dx, but I don't know how to make a delta symbol))


Edit: oops lol I typed that whole thing up before there were any replies, but forgot to hit post.
Yeah if this is suppose to be defintion of g', then g' is negative, so g is decreasing (A).

 

[churchdoesmatter]

thanks guy, i guess majority wins .. A

 

[element]

How do you know its not concave downwards? Just because it's negatve at 3 doesn't mean its a straight line with negative slope. you need to graph the function to be sure. had the possible answers only been increasing decreasing, then obviously its decreasing. But it COULD be concave downwards couldn't it?

If you're taking calculus a must have is a graphing calculator. You need to enter in this function and graph it, then take a look near 3 to see what the function is doing.

 

[element]

In case it wasn't clear, what I mean is that a concave downwards function is also a decreasing function. So it could be D also.

 

[Ns1]

<< n case it wasn't clear, what I mean is that a concave downwards function is also a decreasing function. So it could be D also. >>



that is not true

it can be decreasing and concave up, you dont' know


<< If you're taking calculus a must have is a graphing calculator. You need to enter in this function and graph it, then take a look near 3 to see what the function is doing. >>


most calc classes won't let you use a graphic calculator on a test anyway, better to do it by hand

 

[element]

<<

<< n case it wasn't clear, what I mean is that a concave downwards function is also a decreasing function. So it could be D also. >>



that is not true

it can be decreasing and concave up, you dont' know


<< If you're taking calculus a must have is a graphing calculator. You need to enter in this function and graph it, then take a look near 3 to see what the function is doing. >>


most calc classes won't let you use a graphic calculator on a test anyway, better to do it by hand >>



First of all I'm talking about concave down functions, and you brought up a concave up function, so you're talking about something completely different.
A concave downwards function could be increasing or decreasing or both depending on where in the function you're talking about. In this case we are talking about the function as it approaches 3. And its derivative there is negative. So it is decreasing at that point.

Thought the statement I made was improperly worded too. I meant to say a concave downwards function COULD be a decreasing function, not IS.

In any event my opinion that it needs to be graphed still stands, and that the answer is not as obvious as those who have jumped to conclusions early on make it seem.

When I took calc classes we were allowed to use graphing calculators, as a matter of fact were required to. Why do something by hand that you can have a calculator do for you. Anyone can plug numbers into an equation and create a table and graph them by hand. But you are trying to learn calculus, you shouldn't be wasting time graphing a function. Is this for a college course or AP calc in high school?

 

[Ns1]

both my ap and college calc class did not allow graphing calculators


and the way you phrased your statement it sounded like you were saying "because it is a decreasing function it is a concave down function", sorry for the misunderstanding


and 1 more thing

it's easier to find the vert/hoizontal asymptotes, increasing/decreasing, concave up and concave down and then drawing the graph than it is to plot points

 

[Noriaki]

element®: You may or may not be right.

If i'm reading this right now the question is:

lim [ g(3) - g(x) ] / [ 3 - x ] as x -> 3 = -0.6... (is < 0).

The only conclusion we can draw from that is that the function is decreasing at the point x=3.

To determine concavity we need the second dirivitive.

One of A or B is true (in this case A), since they ask about the value of the first dirivitive.

One of C or D is also true (unless x=3 happens to be a infelction point of this graph), but without a second dirivitive there is no way to tell which of C or D is true.

E would require the dirivitive to be 0 (which it's not, it's negative) and the second dirivitive (which, again, we know nothing about) be positive.

Assuming this is a multiple choice question on a test, the appropriate answer is A.
It is not the only thing that will be true of this graph, but it is the only appropriate answer we can draw from the given information in a multiple choice style, which is what I assumed it to be.