Solved: The formula derived in Exercise 5, expresses the
Chapter 12, Problem 24E(choose chapter or problem)
The formula
\(\kappa(x)=\frac{\left|f^{\prime \prime}(x)\right|}{\left[1+\left(f^{\prime}(x)\right)^{2}\right]^{3 / 2}}\)
derived in Exercise \(5\), expresses the curvature \(\kappa(x)\) of a twice differentiable plane curve \(y=f(x)\) as a function of \(x\). Find the curvature function of each of the curves in Exercises \(23-26\). Then graph \(f(x)\) together with \(\kappa(x)\) over the given interval. You will find some surprises.
\(y=x^{4} / 4, \quad-2 \leq x \leq 2\)
Equation Transcription:
Text Transcription:
kappa(x) = |f^prime prime (x)| / [1 + (f^prime (x))^2]^3/2
5
kappa(x)
y = f(x)
x
23 - 26
f(x)
y = x^4 / 4, -2 leq x leq 2
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