At what point does the curve have maximum curvature? y = 5 ln ⁡ (...

Erick Wyatt

Erick Wyatt

Answered

2022-11-26

At what point does the curve have maximum curvature?
y = 5 ln ( x )
( x , y ) = ( , )
κ(x) approaches ________ as x ?

Answer & Explanation

Desirae Wu

Desirae Wu

Expert

2022-11-27Added 10 answers

Please see the solution and If you have any doubt Please comment
Thanks
н = 5 ln x
curvature = | f ( x ) | [ 1 + f ( x ) 2 ] 3 2
y = f ( x ) f ( x ) = 5 x f ( x ) = 5 x 2 k ( x ) = | 5 x 2 | [ 1 + 25 x 2 ] 3 2 = 5 x ( x 2 + 25 ) 3 2
for max curvature
k ( x ) = 0
k ( x ) = d d x 5 x ( x 2 + 25 ) 3 2 = 5 ( 25 2 x 2 ) ( 25 + x 2 ) 5 2 = 0
x 2 = 25 2 x = ± 25 2 = ± 5 2
x negative so
point where maximum curveture
( 5 2 , 5 ln ( 5 2 ) ) = ( 3.5355 , 6 , 3143 )
lim x k ( x ) = lim x 5 x ( x 2 + 25 ) 3 2 = 0

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