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

Question

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

Desirae Wu · Accepted Answer

Please see the solution and If you have any doubt Please commentThanks      н    =  5  ln  ⁡  xcurvature =                     |                    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 sopoint 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

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

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