Max vs Integral

Calculus Level 3

Let \( f: [0,1] \rightarrow \mathbb{R} \) be a continuous, differentiable function. Define

\[ A = \max { |f(x)| } \text{ or } B = \int_0^1 | f'(x) | + | f(x) | \, dx \]

Which of the following inequalities is always correct?

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