(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A) Find all points on the graph of f(x)=x^2 with tangent lines passing through the point (5,0).

B) Show that no line tangent to g(x)=1/x passes through the origin.

These are problems from a lab problem solving assignment.

2. Relevant equations

y=mx+b

f`(x) = (f(x+h) - f(x)) / h

Not sure what to put, so excuse those functions if they aren't relevant.

3. The attempt at a solution

Well I understand what each graph looks like, but I am completely clueless as to how to approach this problem. I tried looking to my book for some sort of example, but can't find anything that directly relates to this sort of problem. I imagine the x-coordinates for problem A would have to be greater than 5. That's about as far as I can get. If I ask my professor about any of these problems she simply tells me to "think about it."

Question B:

It is apparent, by looking at the graph, that there is no tangent line that will pass through g(x)=1/x. I don't know how to show that though. There is a horizontal asymptote at y=0 and a vertical asymptote at x=0. So no tangent line could pass through the origin (though it would come very close). How would I show this?

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# Calculus I - Tangent Lines

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