Is concave up or down?

A function is concave up (or convex) if it bends upwards. A function is concave down (or just concave) if it bends downwards. I personally would always mix these two up.

How do you know if concave up or down?

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 and concave down at a point if the tangent line lies above the graph in the vicinity of the point.

Is negative concave up or down?

This is equivalent to the derivative of f′ , which is f′′f, start superscript, prime, prime, end superscript, being positive. Similarly, f is concave down (or downwards) where the derivative f′ is decreasing (or equivalently, f′′f, start superscript, prime, prime, end superscript is negative).

Is concave up increasing or decreasing?

So, a function is concave up if it “opens” up and the function is concave down if it “opens” down. Notice as well that concavity has nothing to do with increasing or decreasing.

Is concave up the same as convex?

A function is concave up (or convex) if it bends upwards. A function is concave down (or just concave) if it bends downwards.

Does concave down means convex?

Concave down then equals convex up, meaning that the curve is lower part of a concave epigraph or the upper part of a convex hypograph. Hope this helps!

Why do we concave up?

If a function is decreasing and concave up, then its rate of decrease is slowing; it is “leveling off.” If the function is increasing and concave up, then the rate of increase is increasing. The function is increasing at a faster and faster rate. Now consider a function which is concave down.