Question

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

Answer 1

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.

Answer 2

Draw/imagine the tangent line.

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

yes

Answer 8

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

Answer 9

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

Answer 10

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