Essential Knowledge 2.3B2

Essential Knowledge 2.3B2 Students will know that the tangent line is the graph of a locally linear approximation of the function near the point of tangency.

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I'd never heard of this "locally linear" term, but fortunately I know what they mean. The idea is this:

• Using the gadget blow, pick place on the curve to move the tangent line

• Zoom in on this point (scroll wheel on mouse)

• Keep zooming in

• Eventually you'll see that the graph starts to look just like the tangent line

That's why they call the tangent line a locally linear approximation. If you zoom in on the function, it eventually looks like the tangent line, therefore the tangent line is a pretty good approximation.