In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The depth of water in a storage tank, H H\,H metres, at time t t\,t hours after midnight is modelled by the equation
H=6+4cost2+sint,0≤t≤2π H = \frac{6 + 4 \cos t}{2 + \sin t}, \quad 0 \le t \le 2\pi H=2+sint6+4cost,0≤t≤2πThe point M M\,M on the curve represents the time at which the water depth reaches its local minimum.
Show that the ttt-coordinate of M M\,M is a solution of the equation
4sint+3cost=−2 4 \sin t + 3 \cos t = -2 4sint+3cost=−2Hence find, to 3 significant figures, the ttt-coordinate of MMM.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 327 questions covering 12.1 Gradients of Curves, 12.2 Differentiation from first principles, 12.3 Differentiating x^n, 12.4 Differentiating Quadratics, 12.5 Differentiating functions with two or more terms, 12.6 Gradients, Tangents and Normals, 12.7 Increasing and Decreasing Functions, 12.8 Second Order Derivatives, 12.9 Stationary Points, 12.10 Sketching Gradient Functions, and 12.11 Modelling with Differentiation, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
