Chapter 3: Applications of Differentiation
Section 3.5: Curvature of a Plane Curve
Example 3.5.3
Obtain and graph the curvature κx for y=x2.
Solution
Type yx=… Context Panel: Assign Function
yx=x2→assign as functiony
Write the formula for curvature.
Context Panel: Evaluate and Display Inline
y″x1+y′x23/2 = 21+4x23/2
Figure 3.5.3(a) contains a graph of κx, the curvature function for y=x2.
Figure 3.5.3(a) can be obtained interactively via the Context Panel options Plot Builder≻2-D plot.
The maximum curvature (2) occurs at the origin, and as x increases, the curvature decreases toward zero.
Figure 3.5.3(a) Curvature of y=x2
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