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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.