Using the critical point concept, it is found that f(x) has a horizontal tangent at x = 2 and at x = 7.
What are the critical points of a function?
The critical points of a function are the values of x for which:
[tex]f^{\prime}(x) = 0[/tex]
At these points, the behavior of the function changes from increasing to decreasing or vice-versa, and the tangent is horizontal.
Looking at the graph given in this problem, we see that the behavior changes from increasing to decreasing at x = 2, and from decreasing to increasing at x = 7, hence these are the values of x for which the tangent is horizontal.
You can learn more about the critical point concept at https://brainly.com/question/17087524
