Consider the following statements: I. The function is <strong>DIFFERENTIABLE</strong> at x=3. II. The function is <strong>DIFFERENTIABLE</strong> at x=4. Which of the statements given above is/are correct?
For the following two (02) items: Let the function f(x)=|x-3|+|x-4| be defined on the interval .
- A. I only
- B. II only
- C. Both I and II
- D. Neither I nor II ✓
Correct Answer: D. Neither I nor II
Explanation
The function f(x) = |x-3| + |x-4| has critical points at x=3 and x=4. Since the left-hand limit and right-hand limit of the derivative differ at these sharp corners, the function is non-differentiable at both points.
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