# Portfolio HELP!

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so our teacher told us to do a portfolio on tangents and derivatives and i need help with this first question

Can there be tangents if we glue two functions together?

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Could you post more about the IA so we can help you. Can you scan the question page? or at least detail a little bit more about the problem so that we can understand what you're trying to ask.

Here's the scan

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Ok, so what aspect of the problem don't you understand?

To understand this problem a little bit better I advise, for the first example, drawing 3x^2+3 and x^2+3 on your calculator. Then you can see the difference between the gradients of the two parabolas and see that they cut in half and joined or glued at point (0,3).

The actual question it is posing is can you find other examples of this? To do that, why not get your calculator and try finding some other examples, try forming different graphs and see if they have a common tangent.

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would this be a good example?

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Not necessarily. Just because those two functions intersect it does not mean that they have a common tangent line at some point. Whilst if you glued those two graphs together, it would probably look like it has a common tangent; but if you zoomed in, you would see a point in the line which has a sudden change in gradient. The idea is that you find two different functions which has a common tangent or two functions which have a common gradient at some point. This common gradient is what allows you to "glue" the two different functions together without out it changing suddenly like the third example on the task sheet.

Keep looking! That was a good attempt. Also, try and think of why the examples on the task sheet have a common gradient. What is it about their formula that might cause this? Then how might you replicate to find more examples (if there are any)?

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Ok, so what aspect of the problem don't you understand?

To understand this problem a little bit better I advise, for the first example, drawing 3x^2+3 and x^2+3 on your calculator. Then you can see the difference between the gradients of the two parabolas and see that they cut in half and joined or glued at point (0,3).

The actual question it is posing is can you find other examples of this? To do that, why not get your calculator and try finding some other examples, try forming different graphs and see if they have a common tangent.

Can I ask you something, Sublime Sunshine? Where did you get those functions from? Did you somehow find them using calculations etc. or did you randomly choose them?

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