#MathProblemOfTheDay: Skateparks and Concavity

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Skateparks are a great place to observe concavity.

A curve is concave up if its slope is increasing. This could mean the curve has a positive slope and it’s getting steeper, or it has a negative slope and it’s getting flatter. In both cases, we say the slope is increasing because it’s getting more positive. (Think about how -10 –> -7 is an increase just the way 7 –> 10 is.)

A curve is concave down if the opposite is true: the slope is decreasing. Either it has a positive slope and it’s getting flatter…. or it has a negative slope and it’s getting steeper.

Visually, you can think of a positive slope as an uphill, and a negative slope as a downhill.

A point of inflection is where the concavity changes from down to up, or from up to down.

Where is the point of inflection on this skateboard ramp?

P.S.  What would be the concavity of a straight line?