The function f(x) = |x| is differentiable at x = 0?
Practice Questions
1 question
Q1
The function f(x) = |x| is differentiable at x = 0?
Yes
No
Only from the right
Only from the left
f(x) = |x| is not differentiable at x = 0 because the left-hand and right-hand derivatives do not match.
Questions & Step-by-step Solutions
1 item
Q
Q: The function f(x) = |x| is differentiable at x = 0?
Solution: f(x) = |x| is not differentiable at x = 0 because the left-hand and right-hand derivatives do not match.
Steps: 6
Step 1: Understand what differentiable means. A function is differentiable at a point if it has a defined slope (derivative) at that point.
Step 2: Look at the function f(x) = |x|. This function has two parts: when x is positive (f(x) = x) and when x is negative (f(x) = -x).
Step 3: Find the left-hand derivative at x = 0. This means looking at values of x that are slightly less than 0. The slope (derivative) from the left is -1.
Step 4: Find the right-hand derivative at x = 0. This means looking at values of x that are slightly more than 0. The slope (derivative) from the right is +1.
Step 5: Compare the left-hand and right-hand derivatives. The left-hand derivative is -1 and the right-hand derivative is +1.
Step 6: Since the left-hand and right-hand derivatives do not match (-1 ≠ +1), the function f(x) = |x| is not differentiable at x = 0.
