Find parameter from gradient condition

A question is this type if and only if it asks to find the parameter value(s) where the gradient equals a specific value or satisfies a condition (e.g. parallel to axis, equals 2).

1 questions · Standard +0.3

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AQA Paper 1 2019 June Q15
13 marks Standard +0.3
At time \(t\) hours after a high tide, the height, \(h\) metres, of the tide and the velocity, \(v\) knots, of the tidal flow can be modelled using the parametric equations $$v = 4 - \left(\frac{2t}{3} - 2\right)^2$$ $$h = 3 - 2\sqrt[3]{t - 3}$$ High tides and low tides occur alternately when the velocity of the tidal flow is zero. A high tide occurs at 2am.
    1. Use the model to find the height of this high tide. [1 mark]
    2. Find the time of the first low tide after 2am. [3 marks]
    3. Find the height of this low tide. [1 mark]
  2. Use the model to find the height of the tide when it is flowing with maximum velocity. [3 marks]
  3. Comment on the validity of the model. [2 marks]