Question

use the graph of f in the figure to do the following.

1. find the values of x in the interval (0,5) at which f is not continuous.

b. find the values of x in the interval (0,5) at which f is not differentiable.
a. in the interval (0,5), f is not continuous at x =
(use a comma to separate answers as needed.)

Explanation:

Step1: Identify discontinuity points

A function is discontinuous where there is a break, hole, or jump. On the graph in (0,5), at $x=2$, there is a hole (open circle) with a different filled point, so the function has a discontinuity here.

Step2: Identify non-differentiable points

A function is not differentiable where it is discontinuous, has a corner, or a vertical tangent.

• At $x=2$: Discontinuity means non-differentiable.
• At $x=3$: The graph has a sharp corner (sudden change in slope), so it is non-differentiable here.

Answer:

a. $x=2$
b. $x=2, x=3$