Concavity graph (1 Viewer)

[talulahbay]

I keep getting this grpah the worng way around can anyone answer and explain it?
sketch a curve where y"<0 for x>1 and y">0 for x<1. thankyouu

 

[Drongoski]

That means, the graph is concave down for part of graph to the right of (the vertical line, if you like) x=1, and concave up(like the graph of y = x^2) to the left of x=1.

If you are familiar with the graph of y = x^3, it is the other way round: concave down left of x=0 and concave up, to the right of x=0.

 

[talulahbay]

Is a concave down graph shaped like an unhappy face and concave up shaped like a happy face? Because in the text book it says y">0 the curve is concave up, so the graph should look like a happy face before x=1 and then look like an unhappy face after x=1? because when i drew that it was he same shape as the y=x^3

 

[jarrodoliver1]

Is a concave down graph shaped like an unhappy face and concave up shaped like a happy face? Because in the text book it says y">0 the curve is concave up, so the graph should look like a happy face before x=1 and then look like an unhappy face after x=1? because when i drew that it was he same shape as the y=x^3

Yes. When y''<0 it is concave down (sad face), but when y''>0, the grave is concave up (happy face).