Vault Of Euclid

Concavity of a Parametric Curve with Logarithms

Parametric equations and vector functions core

Determine the concavity of the curve \(x = 2t + \ln t, y = 2t - \ln t\).

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What you need first

derivatives of logarithmic functions
the quotient rule
the relationship between concavity and the second derivative

What this problem tests

Tests the student's ability to correctly apply the formula for the second derivative of a parametric curve and analyze its sign.

This problem is typical of a Calculus II or Multivariable Calculus course when introducing calculus on parametric curves.

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