Linear approximation is a useful tool because it allows us to estimate values on a curved graph (difficult to calculate), using values on a line (easy to calculate) that happens to be close by. If we want to calculate the value of the curved graph at a particular point, but we don’t know the equation of the curved graph, we can draw a line that’s tangent to the curved graph at the point we’re interested in. Remember that “tangent to the graph” means that the line barely skims the graph and touches it at only one point.
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