Side-by-Side Interactive: Dynamic Figure 3.2.5
?
This dynamic figure shows three graphs. Graph (A) is the graph of
y=f(x)
. Use the slider on the right to toggle between Graph (B) or Graph (C), one of which is the graph of the derivative of
f
. Drag the movable point along Graph (A) to show the tangent line to the curve at that point. The
x
-coordinate corresponding to the movable point is shown on Graph (B) or Graph (C). Which statement is true about the derivative when the tangent line is horizontal?
?
The derivative is
+\infty
. The derivative must be 0 . The derivative function itself must have a maximum or minimum value. The derivative does not exist.