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jennychan12
How can you tell just by looking at a graph whether a function is concave up or down?
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.
Draw/imagine the tangent line.
If the tangent line is below it, then it is concave up.
imagine you are riding a bike along the curve from left to right if you are leaning left, it is concave up
ok, thanks. so if the tangent line is above the graph, it's concave down, right?
@satellite73 wow :) that actually made sense, and good analogy! :) so if ur leaning right, it's concave down?
:"concave up" strikes me as devoid of meaning if it is "up" and "down" why bother with the "concave" part
yes..or imagine if you poured water into the line...would the water get collected...or just flow off?
real definition is that any secant line lies entirely above the curve or anyway what you get when you write that in math