How do you determine if a curve is concave up or down?
Answers
Concave upward is when the slope increases
A graph is said to be concave up at a point if the tangent line to the graph at that point lies below the graph in the vicinity of the point .
Concave downward is when the slope decreases
concave down at a point if the tangent line lies above the graph in the vicinity of the point
In general, note that regardless of the sign of the slope (positive, negative or zero), the slopes of the tangent are decreasing as we move from left to right when the graph is concave down and increasing (from left to right) when it is concave up.
Remembering Which way is which? Think: of CUP [C...UP ]
The graph of y = f (x) is concave upward on those intervals where y = f "(x) > 0.
The graph of y = f (x) is concave downward on those intervals where y = f "(x) < 0.