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Chapter 3 | Derivatives
Solution The solution is shown in the following graph. Observe that f ( x ) is increasing and f ′( x ) >0 on ( – 2, 3). Also, f ( x ) is decreasing and f ′( x ) <0 on (−∞, −2) andon (3, +∞). Also note that f ( x ) has horizontal tangents at – 2 and 3, and f ′(−2) =0 and f ′(3) =0.
Sketch the graph of f ( x ) = x 2 −4. On what interval is the graph of f ′( x ) above the x -axis?
3.7
Derivatives and Continuity Now that we can graph a derivative, let’s examine the behavior of the graphs. First, we consider the relationship between differentiability and continuity. We will see that if a function is differentiable at a point, it must be continuous there;
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