Be the Professor Blog #4

Hello Class!
My name is Professor Sarah Davies but i'm cool with just Sarah. Today we are going to be talking about concavity in terms of graphs and how it appears. 

Concavity refers to the curve of a function on a graph. More so it is the direction of the curve. If it is concave up it means that the curve looks like a bowl. If the graph is concave down the graph resembles a frown or an upside-down "U".  In some cases the curve may not be that extreme. 

Graphs with concavity have four different scenarios.

1. Concave up and increasing — where the graph is concave up (looks like a bowl) as x approaches    infinity. 

2. Concave up and decreasing — where the graph is concave up as x approaches negative infinity.

3. Concave down and increasing — where the graph is concave down (looking like an upside down "U") — as x approaches infinity

4. Concave down and decreasing — where the graph is concave down as x approaches negative infinity

To better understand concavity I am going to show you an electricity graph and we are going to able the sections at are either concave up and increasing or decreasing as well as the parts that are concave down and increasing or decreasing.

What is happening from letter to letter?

Beginning to A - 

A to B - 

B to C -

C to D -  

D to E E to F -

F to G - 

G to the End - 

Answers:

Beginning to A - concave up and decreasing

A to B - concave up and increasing 

B to C - concave down and decreasing

C to D - concave down and increasing 

D to E - concave up and decreasing

E to F - concave up and increasing 

F to G - concave up and decreasing

G to the End -  concave up and increasing