1.5 Cusps and Corners. When we determine the derivative of a function, we are differentiating the function. For functions that are “differentiable” for all values of x, the slopes of the tangents change gradually as the point moves along the graph.
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Construct the secant PQ.
Let Q get closer to P and observe the secant line.
QQ on the other side
If the secants approach the same line, as Q approaches P from either side, this line is called the tangent at P.