Chapter 3: Applications of Differentiation

Section 3.5: Curvature of a Plane Curve

	Example 3.5.1
	$$ Show that the curvature of the straight line $y\=m x\+b$ is zero. $$ Solution $$$$ Since the second derivative of a linear function is zero, the numerator in $\mathrm{\kappa }\=\frac{\|y″\|}{{\left(1\+y{\prime }^2\right)}^{3\/2}}$ is zero. Hence, the curvature of a straight line is zero. $$

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