Exercise 10. Show that the curvature of a planar curve which satisfies the equation y = f(r) is given by \f"(x)| K(1) = 3" (Hint: Use the parametrization a(t) = (t, f(t), 0), and use the formula in previous exercise.) Compute the curvatures of y = x, x?, r, and a. %3D

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Q: find a parametrization c(t) of the curve satisfying the given condition.  y = 3x − 4, c(3) = (2, 2)

A: To find the parametrization

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A: Modify the given figure as shown in Figure 1.

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Q: use Eq. (3) to calculate the curvature function κ(t)  r(t) = (t−1, 1, t)

A: Solution:Given     r(t)=(t-1, 1,t)To find κ(t):κ(t)=r'(t)×r''(t)r'(t)3

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Q: 9) Sketch x = indieate the onientatiba of the 2t°, y = 3t, -4sts4 aud with %3D Curve an arow,

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Q: 10.) At what point does the curve have maximum Curvature? y=In(x). K(x)= f"|

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