Questions: Question 3.3 Part 1 of 3 Completed: 13 of 31 My score: 11.9/31 pts (38.4%) Use the graph of f in the figure to do the following: a. 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 c. Sketch a graph of f' a. In the interval (0,5), f is not continuous at x = (Use a comma to separate answers as needed)

Question 3.3 Part 1 of 3 Completed: 13 of 31 My score: 11.9/31 pts (38.4%) Use the graph of f in the figure to do the following: a. 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 c. Sketch a graph of f' a. In the interval (0,5), f is not continuous at x = (Use a comma to separate answers as needed)
Transcript text: Question 3.3 Part 1 of 3 Completed: 13 of 31 My score: 11.9/31 pts (38.4%) Use the graph of f in the figure to do the following: a. 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 c. Sketch a graph of f' a. In the interval (0,5), f is not continuous at x = (Use a comma to separate answers as needed)
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Solution

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Solution Steps

Step 1: Identify the Intervals of Discontinuity
  • Examine the graph to identify where the function is not continuous in the interval (0,5).
  • Look for points where there are breaks, jumps, or holes in the graph.
Step 2: List the Points of Discontinuity
  • From the graph, note down the x-values where the function is not continuous.
  • These are the points where the function either jumps to a different value or has a hole.
Step 3: Verify the Discontinuity Points
  • Confirm that the identified points are indeed discontinuities by checking the left-hand and right-hand limits at those points.
  • Ensure that the function does not meet the criteria for continuity at these points.

Final Answer

The function is not continuous at \( x = 1, 3, 4 \) in the interval (0,5).

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