Determine the point at which the function f(x) = |x - 3| is not differentiable.

Determine the point at which the function f(x) = |x - 3| is not differentiable.

Step 1: Understand what differentiability means. A function is differentiable at a point if it has a defined slope (or derivative) at that point.
Step 2: Look at the function f(x) = |x - 3|. This function represents the absolute value of (x - 3).
Step 3: Identify where the function changes. The expression inside the absolute value, (x - 3), equals zero when x = 3. This is where the function changes from negative to positive.
Step 4: Analyze the graph of the function. The graph of f(x) = |x - 3| has a V-shape with a sharp corner at the point (3, 0).
Step 5: Recognize that at the sharp corner (x = 3), the slope changes abruptly. This means the derivative does not exist at this point.
Step 6: Conclude that the function f(x) = |x - 3| is not differentiable at x = 3.

Absolute Value Function – The function f(x) = |x - 3| represents an absolute value function, which has a V-shape and is continuous everywhere but not differentiable at the vertex.
Differentiability – A function is differentiable at a point if it has a defined derivative there; sharp corners or cusps indicate points of non-differentiability.