Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

TGM Original Questions

The equation of a curve is \(y = \ln\left( \frac{3x - 7}{x + 1} \right)\).

  1. Find, respectively, the equations of the tangent and the normal to the curve at the point where the curve crosses the \(x\)-axis.
  2. Hence find the area of the triangle formed by the tangent and the normal to the curve at the above point and the \(y\)-axis.

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Answer:(i) Tangent: \(y=\dfrac25(x-4)\); normal: \(y=-\dfrac52(x-4)\) (ii) \(\dfrac{116}{5}\text{ units}^2\)

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