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Trigonometry
Question

A formula for the curvature of the graph of a fun...

A formula for the curvature of the graph of a function in the \(x y\) -plane

a. The graph \(y = f ( x )\) in the \(x y\) -plane automatically has the parametrization \(x = x , y = f ( x )\) , and the vector formula \(r ( x ) = x i + f ( x ) j\) . Use this formula to show that if \(f\) is a twice-differentiable function of \(x\) , then \(\kappa ( x ) = \frac { | f ^ { \prime \prime } ( x ) | } { [ 1 + ( f ^ { \prime } ( x ) ) ^ { 2 } ] ^ { 3 / 2 } }\) .

Answer

\(\text { (b) } \cos x\)

Solution
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