Problem 3.4. [3 pts] Let $f(x)$ be a sufficiently many times differentiable (twice is enough) single variable real valued function. Find the curvature of the graph of $f$, living in $xy$-plane, as a formula just in terms of $f$ and its higher derivatives.
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The function $f(x)$ is sufficiently many times differentiable (at least twice). We need to express the curvature as a formula in terms of $f$ and its higher derivatives. The graph of a function $y = f(x)$ can be parameterized as a curve in the $xy$-plane. Let the Show more…
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