Question

For the graph shown, identify a) the point(s) of inflection and b) the intervals where the function is concave up or concave down. 10 0 0 5 ilm EX m. mil -10 WO 110 a) The point(s) of inflection is/are (Type an ordered pair. Use a comma to separate answers as needed.)

Answer 1

a) Point of inflection is (3, 8)

b) The function is concave up in the interval where x < 4.

The function is convex down in the interval where x ≥ 2

Step-by-step explanation

a) Points of Inflection

These are the points on the graph where concavity changes. That is, the graph changes from concave up form to convex down form or from convex down form to concave up form.

From this portion of the graph attached, we can see that this graph changes from concave to convex form around the point where

x = 3 and y = 8.

In ordered pair form, (3, 8)

b) Intervals where the function is concave up and intervals where the function is convex down.

We can see that the function is concave up at values of x less than 4. So, the interval where the graph is concave up is x < 4.

And we can see that the function is convex down from the point where x = 2 upwards. So, the function is convex down in the interval where x ≥ 2

Hope this Helps!!!