Tangent Lines

[Index]

Use the graph to estimate the slope of the tangent line, if it exists, to the graph at the given point.
x = 0

The answer given is h + 4.

I am terrible with graphs. I have no idea how to even begin. Everything I've looked up so far has been way too confusing. (Sorry for my crude drawing.)

 

[wjm11]

hello, Index,

You really haven't given us enough to help you. First of all, there is no "h" anywhere on your graph, so "h + 4" makes no sense whatsoever.

Some comments: I see a point on the y axis at 2. If you draw a tangent line to the curve you have drawn at that point, the line might be at about a 45 degree angle to the horizontal. This would mean the tangent line has a slope of 1, i.e., that the change in y is equal to the change in x between any two points on the line.

Hope that helps.

 

[Index]

There is no h on the original graph. It is just x and y. However, it is in one of the formulas I found:

 

[mmm4444bot]

Another riddle!

Index, if you're asked to estimate the slope of a line from a graph, then the "estimating" part is simply reading off the coordinates of any two convenient points on the line, as best you can. Once you've got those four numbers, put them into the slope formula.

That's all there is to it.

(Of course, I'm assuming that you know what a tangent line is, and that you can sufficiently draw it on the given graph.)

But, I suspect that you might not have given us all of the information you received.

Did they give you some graph, and you tried to reproduce it for us?

Did they give you some function's definition, and you graphed this function using a machine, and then you tried to reproduce for us what your machine displayed?

If the graph is some such curve through the point (0, 2), then it seems strange, to me, for the posted instruction to make a conditional statement regarding whether or not the slope of the tangent line at that point exists because it obviously exists.

Something doesn't seem right (i.e., a riddle).

Please tell us about everything you received for this exercise.

 

[Index]

They gave me a graph that I tried to reproduce. The instruction is for a set of problems of which this belongs. I have no equation for this graph, only the graph and x = 0.
It seemed like it had the points (0, 2) and (1, 3) in it which would give the slope of 1.

 

[mmm4444bot]

… The instruction is for a set of problems …

Ah, that makes more sense, to me.

Then there is probably going to be at least one tangent line that turns out to be vertical (i.e., it's slope is undefined).

'

… It seemed like [the tangent line contains] the points (0, 2) and (1, 3) in it which would give the slope of 1.

Then it seems to me that you're done with this one.

Good job.