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Match a function to its derivative

The diagrams below show the graph of ff and its derivative f′f^{\prime}. State clearly, with reasons, which is the graph of ff and that of f′f^{\prime}.

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Diagram 1 is positive on the far left, crosses to negative at a negative x and crosses back to positive at x=0. Diagram 2 rises to a maximum at the first zero of Diagram 1, falls to a minimum on the y-axis above the x-axis, then rises sharply. These independent schematics preserve the source qualitative relationships; no numerical formula or extra coordinates are assigned.
Diagram 1 is positive on the far left, crosses to negative at a negative x and crosses back to positive at x=0. Diagram 2 rises to a maximum at the first zero of Diagram 1, falls to a minimum on the y-axis above the x-axis, then rises sharply. These independent schematics preserve the source qualitative relationships; no numerical formula or extra coordinates are assigned.
Diagram 1 is positive on the far left, crosses to negative at a negative x and crosses back to positive at x=0. Diagram 2 rises to a maximum at the first zero of Diagram 1, falls to a minimum on the y-axis above the x-axis, then rises sharply. These independent schematics preserve the source qualitative relationships; no numerical formula or extra coordinates are assigned.

[2007/ACJC/II/1]

CJC · Discussion · Question 1

At a differentiable turning point, look for a zero of the derivative and the correct sign change.

Read the worked solution