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Given a set of curves on axes, generated from a function and its first two derivatives, identify which curve corresponds to which derivative.

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The following graph (which may take a little while to load) shows three curves: a solid line, a dashed line and a dotted line. These curves represent a function and its derivatives; if we call the function \$f\$, then one curve represents \$f\$ and the other two curves represent \$f'\$ and \$f''\$.

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{geogebra_applet('BsRYG6PV',defs)}

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Solid line

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Dashed line

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Dotted line

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\$f\$

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\$f'\$

", "

\$f''\$

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For each curve, select the corresponding derivative. You will score \$2\$ points for each curve correctly identified, and \$-1\$ point for each curve incorrectly identified.

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Here are some questions to consider for this problem.

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• What happens to even functions when you differentiate them? What about odd functions?
• \n
• Can you identify any maxima and minima and line them up with zeroes in other functions?
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", "type": "question", "contributors": [{"name": "Philip Walker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/362/"}]}]}], "contributors": [{"name": "Philip Walker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/362/"}]}