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There are two main ways of thinking about this. Different people have different preferences.

1) This is identical to being asked: \"A displacement-time graph is given, select the corresponding velocity-time graph\".  Hence use the same reasoning as in previous questions (when is the velocity positive, negative, zero.)

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2) The derivative tells you about the gradient of the original graph. Thus, you want to ask yourself \"when is the gradient positive, when is the gradient negative, when is the gradient zero\".

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A graph is drawn. A student is to identify the derivative of this graph from four other graphs. There are four version of this question: I: cubic, II: linear, III: quadratic, IV: sinusoisal.

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Select the graph that shows the derivative of of the graph above.

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