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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