Posted by Jaime on .
This is a three-part question:
a. the graph y = f(x) in the xy-plane has parametrization x=x, y=f(x), and vector formula r(x) = xi + f(x)j. Use this to show that if f is twice-differentiable, then
b. use the formula for k in part a to find the curvature of y = ln(cosx) when -pi/2 < x < pi/2.
c. show that the curvature is zero at the point of inflection.
You left out something in (a) There is no = sign. It looks like you are trying to compute the curvature of the y = f(x) line, which is defined as the reciprocal of the radius of curvature, or d(phi)/ds, where phi is the slope and x is the arc length.
I suggest you review derivations such as the ones at