Determine whether the function is continuous or differentiable for given input values.
A) The function is continuous on the input interval shown, but it is not differentiable at x = 4.
B) The function is continuous on the input interval shown, but it is not differentiable at x = 6.
C) The function is not continuous on the input interval shown, but it is not differentiable at x = 6.
D) The function is not continuous on the input interval shown, but it is not differentiable at x = 4.
E) The function is both continuous and differentiable at x = 4.

Question

Determine whether the function is continuous or differentiable for given input values. 
A) The function is continuous on the input interval shown, but it is not differentiable at x = 4. 
B) The function is continuous on the input interval shown, but it is not differentiable at x = 6. 
C) The function is not continuous on the input interval shown, but it is not differentiable at x = 6. 
D) The function is not continuous on the input interval shown, but it is not differentiable at x = 4. 
E) The function is both continuous and differentiable at x = 4.

Quizplus · Accepted Answer

From the graph, we can see that the function is continuous on the input interval shown as there are no breaks, jumps or holes. However, at x = 4, the graph has a sharp corner, indicating that the function is not differentiable at x = 4. Therefore, the correct choice is A.

Determine Whether the Function Is Continuous or Differentiable for Given