Find the curvature of the given function at the indicated value of $X$ : $f ( x ) = \cos ( x ) , x = 0$
A) $\frac { 1 } { 2 ^ { \frac { 3 } { 2 } } }$
B) 0
C) 1
D) Undefined

Question

Quizplus · Accepted Answer

The curvature $\kappa$ of a function $y = f(x)$ at a point is given by $\kappa = \frac{|f''(x)|}{(1 + (f'(x))^2)^{\frac{3}{2}}}$. For $f(x) = \cos(x)$, $f'(x) = -\sin(x)$ and $f''(x) = -\cos(x)$. At $x = 0$, $f'(0) = 0$ and $f''(0) = -1$, so $\kappa = \frac{|-1|}{(1 + (0)^2)^{\frac{3}{2}}} = 1$.

Find the Curvature of the Given Function at the Indicated XXX

Find the Curvature of the Given Function at the Indicated $X$