Using the following graph explain the behavior of function f

Using the following graph, explain the behavior of function f on the interval from x = 0 to x = 10.

State over which intervals f is increasing or decreasing and concave up or concave down. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

Increasing ______________

Decreasing ____________

Concave up ______________

Concave down______________

Solution

From the graph, we can see that tangent to the given curve has positive slope over the given interval.

It means graph of the function is always increasing over the given interval.

We can see that graph is changing their shape at point p(x=5).

and graph has concave up for ( 0 , 5 )

and concave down for ( 5 , 10).