- #1

- 342

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"A cubic function y=ax

^{3}+bx

^{2}+cx+1 has only one tangent which has the slope of 4, and which touches the graph in x=-1/3"

I did the best I could to translate it into English. The problem went on ofcourse, but this is the part which raised the following question in my head:

shouldnt a cubic function like this have 2 tangents with the same slope in every 2 according points on the graph, EXCEPT for the extremum point?

Where do I go wrong?

When you solved the problem, you got that y=3x

^{3}+9x

^{2}+9x+1

You can easily draw it out on http://rechneronline.de/function-graphs/

Thanks in advance