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No. When you first start learning about derivatives, you are told you draw a line tangent to a point and then find the slope of that line at that point. The sl
by klunger 11y ago
No. When you first start learning about derivatives, you are told you draw a line tangent to a point and then find the slope of that line at that point. The slope is just del y / del x. So, if del x = 1, then the slope is just del y / 1 = del y = the height of the triangle.
Of course, it is more useful to get a derivative as a function of x, so you don't have to do this at every point. But, as a starting point, when you are first learning about derivatives and only have a background in algebra and geometry, this is a nice way to think about it.
- weland 11y agoRight. My browser didn't play nice with MathML, so I missed about the part where x = 1 (i.e. I couldn't see the "1" :) ) My objection was that a tangent line, as opposed to a segment, has infinite length. I can draw infinitely many segments tangent to the curve -- and get infinitely many heights for it.
- klunger 11y agoAh, ok. That makes sense. Confusion resolved!