For the function f(x) = |x - 2| + |x + 3|, find the point where it is not differ

For the function f(x) = |x - 2| + |x + 3|, find the point where it is not differentiable.

For the function f(x) = |x - 2| + |x + 3|, find the point where it is not differentiable.

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.

Absolute Value Functions – The function involves absolute value expressions, which can create points of non-differentiability at the points where the expression inside the absolute value equals zero.
Differentiability – Understanding the conditions under which a function is differentiable, particularly at points where the function changes its definition.