Discussion
Which of the following is NOT true?
Answer: B
The statement that is not true is that every continuous function is differentiable. The function \(f(x) = |x|\) is continuous at \(0\) but has a corner there, so its derivative does not exist at \(0\). The opposite statement, that every differentiable function is continuous, is a standard theorem and is true.
The function \(|x| + \sin|x-3|\) is a sum of continuous functions, so it is continuous, and it has corners at \(x = 0\) and \(x = 3\) where the absolute values change sign, so it is not differentiable there. Both of those statements are true, which leaves option B as the false one.
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