For the function f(x) = |x - 2| + |x + 3|, find the point where it is not differentiable.
Practice Questions
1 question
Q1
For the function f(x) = |x - 2| + |x + 3|, find the point where it is not differentiable.
-3
2
0
1
The function is not differentiable at x = -3 and x = 2, but the first point of interest is -3.
Questions & Step-by-step Solutions
1 item
Q
Q: For the function f(x) = |x - 2| + |x + 3|, find the point where it is not differentiable.
Solution: The function is not differentiable at x = -3 and x = 2, but the first point of interest is -3.
Steps: 6
Step 1: Understand the function f(x) = |x - 2| + |x + 3|. This function has absolute value terms.
Step 2: Identify where each absolute value term changes. The term |x - 2| changes at x = 2, and |x + 3| changes at x = -3.
Step 3: List the points where the function could be non-differentiable. These points are x = -3 and x = 2.
Step 4: Check the behavior of the function around these points. At x = -3, the function changes from one linear piece to another, indicating a potential non-differentiability.
Step 5: Similarly, check at x = 2. The function also changes here, indicating it is not differentiable at this point as well.
Step 6: Conclude that the function is not differentiable at both x = -3 and x = 2, but the first point of interest is x = -3.
