Consider the graph of the fund ion y =p( x) that is provided in Figure 1.12. Ass
ID: 2873323 • Letter: C
Question
Consider the graph of the fund ion y =p( x) that is provided in Figure 1.12. Assume that each portion of the graph of p is a straight line, as pictured At left, the piecewise linear function y = p(.x). At right, axes for plotting y - p'(x). State all values of a for which limxrightarrowa p(x) does not exist. State all values of a for which p is not continuous at a. State ail values of a for which p is not differentiable at x = a. On the axes provided in Figure 1.42, sketch an accurate graph of y = p'(x).Explanation / Answer
From the provided figure:
is not existed and
Thus, means is not exists.
Similarly, is not defined at . Then is also not exists.
Thus, is not exists for .
If or is not exists, thus means is not continuous at .
Therefore, the function is not continuous at .
The function where it fails to continuous, then at the same values, the function is not differentiable.
Also, from the graph is not smooth at . At these values also, is not differentiable.
Therefore, is not differentiable at .