As AP Calculus was ending this morning, we were finding the equation of the tangent line to the square root curve at the point (1,1). I graphed the tangent line and the square root function on the same coordinate plane and then zoomed in really close. What we can notice is that as we zoom in closer and closer to (1,1), the difference between the curve and the tangent line becomes negligible. This is one of the reasons we simplify things by saying the slope of the tangent line is the slope of the curve.
Check out the picture if you're interested.
PS: +5 on a quiz grade if you bring me a printed copy of the picture by Wednesday, 9/23.
PPS: Cambridge Cambridge Cambridge (https://en.wikipedia.org/wiki/Isaac_Newton)
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