# Thread: Sketching a function ????

1. ## Sketching a function ????

I need to sketch a function that is increasing and is concave up on [0,1]

I know the following:

• concave up refers to the second derivative where a<x<b
• Increasing refers to F(x2) > f(x1)
So how do I use the interval info to sketch the graph ? If , 0 is the x- axis & 1 is the y-axis am I making sure that the graph intersects at [0,1] above the x-axis and is heading upwards in order to fulfill the requirements of the question?

If so, where should the tail start ? Can I start it from say ... [-2,0] heading upwards & intersecting at the given interval [0,1] ?

It seems too arbitrary...

2. Originally Posted by kbgemini16
I need to sketch a function that is increasing and is concave up on [0,1]

I know the following:
• concave up refers to the second derivative where a<x<b
• Increasing refers to F(x2) > f(x1)
So how do I use the interval info to sketch the graph ? If , 0 is the x- axis & 1 is the y-axis am I making sure that the graph intersects at [0,1] above the x-axis and is heading upwards in order to fulfill the requirements of the question?

If so, where should the tail start ? Can I start it from say ... [-2,0] heading upwards & intersecting at the given interval [0,1] ?

It seems too arbitrary...
No! Don't start from a random point. Use the interval that you are given, and draw a graph that follows the criteria you are given.

The reason I say this is that you have absolutely NO idea what happens on the other intervals. For all you know, there could be a discontinuity at either one of those points. Just draw a graph that is concave up and increasing. Nothing else matters, no y values are significant, so any sketch that follows these criteria is an acceptable answer. That is, of course, assuming that what you gave is the ONLY information you know.

3. ## To be clear ....

Originally Posted by Kalter Tod
No! Don't start from a random point. Use the interval that you are given, and draw a graph that follows the criteria you are given.

The reason I say this is that you have absolutely NO idea what happens on the other intervals. For all you know, there could be a discontinuity at either one of those points. Just draw a graph that is concave up and increasing. Nothing else matters, no y values are significant, so any sketch that follows these criteria is an acceptable answer. That is, of course, assuming that what you gave is the ONLY information you know.
Are you saying that as long as the point starts at [0,1] and heads upward I am meeting the criteria:
concave up
increasing
no tail is needed ?

4. Originally Posted by kbgemini16
Are you saying that as long as the point starts at [0,1] and heads upward I am meeting the criteria:
concave up
increasing
no tail is needed ?
Well, you have to make it concave up as well, but yes, that's correct. In fact, to put in a "tail" would be incorrect. As I said before, if you are not given a specific function, and are only given an interval, you have no idea what happens outside of that interval. For all we know, the function only exists on the given interval. There could potentially be nothing on either side of the given interval.

P.S. You do know what concave up looks like on a graph, right?

5. ## Concave up ?

Originally Posted by Kalter Tod
Well, you have to make it concave up as well, but yes, that's correct. In fact, to put in a "tail" would be incorrect. As I said before, if you are not given a specific function, and are only given an interval, you have no idea what happens outside of that interval. For all we know, the function only exists on the given interval. There could potentially be nothing on either side of the given interval.

P.S. You do know what concave up looks like on a graph, right?
From the graphs I've seen it's looks like any curve that when tangent lines are drawn have a positive slope. Also it looks like they have to be above the x-axis .

Is that correct ?