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Let $f(x)$ be a twice differentiable function over $[a, b]$ with arc length $l$. show that there exists a value $c \in [a, b]$ such that the angle $\theta$ between the tangent line and the horizontal line at $x = c$ satisfies $|\cos\theta| = \frac{b-a}{l}.$
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Let $f(x)$ be a twice differentiable function over $[a, b]$ with arc length $l$. show that there exi...
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