Determine the point at which the function f(x) = |x - 3| is not differentiable.
Practice Questions
1 question
Q1
Determine the point at which the function f(x) = |x - 3| is not differentiable.
x = 1
x = 2
x = 3
x = 4
The function f(x) = |x - 3| is not differentiable at x = 3 because it has a sharp corner.
Questions & Step-by-step Solutions
1 item
Q
Q: Determine the point at which the function f(x) = |x - 3| is not differentiable.
Solution: The function f(x) = |x - 3| is not differentiable at x = 3 because it has a sharp corner.
Steps: 6
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.
