Unformatted text preview: f and f ′ are given on the right. Which is which? Answer . There are a few telltale signs from which we can draw our conclusion: (a) Note that the red graph has a horizontal tangent when x = 0, while the blue graph is 0 when x = 0. Since the derivative f ′ gives the slopes of the tangents of f , we conclude that the red graph is for f and the blue graph is for f ′ . (b) The red graph is increasing on (2 , 0) and is decreasing on (0 , 4), while the blue graph is positive on (2 , 0) and is negative on (0 , 4). Since the derivative f ′ of f is about the rate of change of f , we see that the red graph is for f and the blue graph is for f ′ ....
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 Fall '08
 DANIELYAN
 Calculus, Derivative, Slope, red graph, Matthew Fleeman, Arbin Rai

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