Discussion
Let \(f(x) = 10 - |x - 5|, x \in \mathbb{R}\) , Then \(f(x)\) is not differentiable at
Answer: D
f is not differentiable at x = 5.
\(|x - 5|\) has a corner where \(x - 5 = 0\): its slope is -1 to the left and +1 to the right. So f has slopes +1 and -1 on the two sides of x = 5, and no single derivative exists there.
Everywhere else f is linear, so it is differentiable at x = 10, 15, -5 and -15. x = 15 and x = -5 are where f(x) = 0, which has nothing to do with differentiability.
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