Chapter 14.5, Problem 50E

Special formula: Curvature for y = f(x) Assume that f is twice differentiable. Prove that the curve y = f(x) has curvature

$\kappa (x)=\frac{|f^{″}(x)|}{{(1+f^{\prime }{(x)}^2)}^{3/2}}.$

(Hint: Use the parametric description x = t, y = f(t).)