\\\\kappa =(|f^('')(x)|)/((1+[f^(')(x)]^(2))^((3)/(2)))

\ b. Let

y=y_(c)+-\\\\sqrt(R^(2)-(x-x_(c))^(2))

be the circle that satisfies the following properties:\ i.

y(x_(0))=f(x_(0))

(the curve

y=f(x)

and the circle intersect at

(x_(0),f(x_(0)))

)\ ii.

y^(')(x_(0))=f^(')(x_(0))

and

y^('')(x_(0))=f^('')(x_(0))

\ Show that

R=(1)/(\\\\kappa )

and find the center,

(x_(c),y_(c))

. This circle is known as the osculating\ circle.

=(1+[f(x)]2)3/2f(x) b. Let y=ycR2(xxc)2 be the circle that satisfies the following properties: i. y(x0)=f(x0) (the curve y=f(x) and the circle intersect at (x0,f(x0)) ) ii. y(x0)=f(x0) and y(x0)=f(x0) Show that R=1/ and find the center, (xc,yc). This circle is known as the osculating circle