Question

If \( f(x) = \max \{3 - x, 3 + x, 6\} \) is not differentiable at \( x = a \) and \( x = b \), then \( |a| + |b| = \)

• A. 4
• B. 5
• C. 6
• D. 8

Hint:

Check points where the expressions inside a max function intersect to find non-differentiable points.

Answer 1

The Correct Option is C

The function \( f(x) = \max \{3 - x, 3 + x, 6\} \) is not differentiable at points where the maximum function switches from one expression to another.
Equating \( 3 - x = 6 \Rightarrow x = -3 \), and \( 3 + x = 6 \Rightarrow x = 3 \).
So, non-differentiability occurs at \( x = -3 \) and \( x = 3 \).
Thus, \( |a| + |b| = |{-3}| + |3| = 3 + 3 = 6 \).