jennychan12 2 years ago How can you tell just by looking at a graph whether a function is concave up or down?

1. Twis7ed

The concavity is basically where it "opens up" to. So, for example, f(x) = x^2 is concave up since it opens upwards while g(x) = -x^2 is concave down since it opens downwards.

2. wio

Draw/imagine the tangent line.

3. wio

If the tangent line is below it, then it is concave up.

4. wio

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5. satellite73

imagine you are riding a bike along the curve from left to right if you are leaning left, it is concave up

6. jennychan12

ok, thanks. so if the tangent line is above the graph, it's concave down, right?

7. jennychan12

@satellite73 wow :) that actually made sense, and good analogy! :) so if ur leaning right, it's concave down?

8. satellite73

yes

9. satellite73

:"concave up" strikes me as devoid of meaning if it is "up" and "down" why bother with the "concave" part

10. johnweldon1993

yes..or imagine if you poured water into the line...would the water get collected...or just flow off?

11. satellite73

real definition is that any secant line lies entirely above the curve or anyway what you get when you write that in math

12. wio

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