Ok, I've found the answer to these questions, but I did so in more of a trial and error way. The question is:(adsbygoogle = window.adsbygoogle || []).push({});

f(x) = 2x^2 + x

Find the two tangent lines to the curve, which both pass through the point (2,-3).

So, I tried using y=mx+b = 2x^2 + x, where m = f'(x) = 2x + 1, thus:

(2x+1)x + b = 2x^2 + x. I worked this out to find an extraneous answer, and one correct tangent of y = -x - 1. I know the other answer has a slope of 11, through trial and error, but there's got to be an easier way.

Any thoughts on how to do this algebraically?

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# Pesky Tangents

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