- #1
bpcraig
- 3
- 0
Hello all,
We know that for some well-behaved, smooth/continuous, twice differentiable function of x, f[x] there exists at each point a slope (f ' [x]) and a radius of curvature
[tex]\rho [x]=\frac{\left(1+f'[x]^2\right)^{\frac{3}{2}}}{f\text{''}[x]}[/tex]
It also seems intuitive to think that at every point on such a function, the tangent line vector and the vector from the center of curvature to this point would be normal to one another.
Is this necessarily true?
We know that for some well-behaved, smooth/continuous, twice differentiable function of x, f[x] there exists at each point a slope (f ' [x]) and a radius of curvature
[tex]\rho [x]=\frac{\left(1+f'[x]^2\right)^{\frac{3}{2}}}{f\text{''}[x]}[/tex]
It also seems intuitive to think that at every point on such a function, the tangent line vector and the vector from the center of curvature to this point would be normal to one another.
Is this necessarily true?