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Q&A Please draw this picture to distinguish between Convex and Concave functions, featuring “bear in a conCAVE” mnemonic?

posted 9mo ago by Glen_b‭ · edited 9mo ago by Glen_b‭

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#3: Post edited by $user avatar$ Glen_b‭ · 2025-12-22T04:19:26Z (9 months ago)

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From the [definitions](https://en.wikipedia.org/wiki/Convex_function), examples of convex and concave functions can look like this:
![Examples of concave and convex curves; convex have the function "below" (at or below) a line joining points on the curve, concave have the function "above"](https://math.codidact.com/uploads/drgkf16wslweomh25dqffwsoh490)
Consequently the mnemonic drawing would be something like this:
![Bear below a conCAVE curve](https://math.codidact.com/uploads/nm5xjizgkc6yloeafasbzmqst4om)

From the [definitions](https://en.wikipedia.org/wiki/Convex_function), examples of convex and concave functions can look like this:
![Examples of concave and convex curves; convex have the function "below" (at or below) a line joining points on the curve, concave have the function "above"](https://math.codidact.com/uploads/drgkf16wslweomh25dqffwsoh490)
In each case, the grey line relates to showing the definition holds, its not part of the function.
Consequently the mnemonic drawing would be something like this:
![Bear below a conCAVE curve](https://math.codidact.com/uploads/nm5xjizgkc6yloeafasbzmqst4om)

#2: Post edited by $user avatar$ Glen_b‭ · 2025-12-22T04:17:54Z (9 months ago)

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From the [definitions](https://en.wikipedia.org/wiki/Convex_function), examples of convex and concave functions can look like this:
![Examples of concave and convex curves; convex have the function "below" (at or below) a line joining points on the curve, concave have the function "above"](https://math.codidact.com/uploads/drgkf16wslweomh25dqffwsoh490)
~~Consequently the mnemomic drawing would be something like this:~~
![Bear below a conCAVE curve](https://math.codidact.com/uploads/nm5xjizgkc6yloeafasbzmqst4om)

From the [definitions](https://en.wikipedia.org/wiki/Convex_function), examples of convex and concave functions can look like this:
![Examples of concave and convex curves; convex have the function "below" (at or below) a line joining points on the curve, concave have the function "above"](https://math.codidact.com/uploads/drgkf16wslweomh25dqffwsoh490)
Consequently the mnemonic drawing would be something like this:
![Bear below a conCAVE curve](https://math.codidact.com/uploads/nm5xjizgkc6yloeafasbzmqst4om)

#1: Initial revision by $user avatar$ Glen_b‭ · 2025-12-22T04:17:22Z (9 months ago)

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From the [definitions](https://en.wikipedia.org/wiki/Convex_function), examples of convex and concave functions can look like this: 

![Examples of concave and convex curves; convex have the function "below" (at or below) a line joining points on the curve, concave have the function "above"](https://math.codidact.com/uploads/drgkf16wslweomh25dqffwsoh490)

Consequently the mnemomic drawing would be something like this:

![Bear below a conCAVE curve](https://math.codidact.com/uploads/nm5xjizgkc6yloeafasbzmqst4om)

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