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. 5 16 HE 10 10 a) The point(s) of inflection is/are (Type an ordered pair. Use a comma to separate answers as needed.)

Answer 1

In an inflection point the curvature of the function changes, in this example we can see that the graph of the function is concave up in the interval:

$(-\infty,2)$

And concave down in the interval:

$(2,\infty)$

Since the plot changes from concave up to concave down at x equals 2 we have an inflection point on that position, and since with an x equals 2 the variable y equals 1, the inflection point would be:

$(2,1)$