Differentiation - Connected Rates of Change

Differentiation - Connected Rates of Change

TGM Original Questions

The equation of a curve is given by \(y = (x - 3)\sqrt{2x + 1}\). A particle moves along the curve such that the \(x\)-coordinate of the particle increases at a constant rate of \(0.15\) unit/s, find

  1. the rate of change of the \(y\)-coordinate of the particle when \(x = 3\), and
  2. the possible \(x\)-coordinate(s) of the particle at the instant(s) when the rate of decrease of the \(y\)-coordinate is twice of the rate of increase of the \(x\)-coordinate.

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Answer:(i) \(\dfrac{3\sqrt7}{20}\text{ unit s}^{-1}\) (ii) \(x=0\)

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