Determine the point at which the function f(x) = |x - 1| is not differentiable.
Practice Questions
1 question
Q1
Determine the point at which the function f(x) = |x - 1| is not differentiable.
x = 0
x = 1
x = 2
x = -1
The function |x - 1| is not differentiable at x = 1 due to a cusp.
Questions & Step-by-step Solutions
1 item
Q
Q: Determine the point at which the function f(x) = |x - 1| is not differentiable.
Solution: The function |x - 1| is not differentiable at x = 1 due to a cusp.
Steps: 5
Step 1: Understand what the function f(x) = |x - 1| means. This function represents the distance between x and 1 on a number line.
Step 2: Identify where the function changes its behavior. The absolute value function has a 'corner' or 'cusp' where the expression inside the absolute value equals zero.
Step 3: Set the inside of the absolute value to zero: x - 1 = 0. Solve for x. This gives x = 1.
Step 4: Recognize that at x = 1, the function has a sharp point (cusp) and does not have a defined slope (derivative) at that point.
Step 5: Conclude that the function f(x) = |x - 1| is not differentiable at x = 1.
