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Derivatives, Tangent Lines and Rates of Change

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1. A curve has the equation x²-4xy+y²=24
a) Show that
dy/dx= (x-2y)/(2x-y)

b) find the equation for the tangent to the curve at the point P (2, 10)
The tangent to the curve at Q is parrallel to the tangent at P
c) find the coordinates of Q

2. The diagram shows the coss-section of a vase. The volume of the water
in the vase, V cm³, when the depth of water in the vase is h cm is given by
V=40 pi (e^0.1 h^-1)
The vase is initially empty and water is poured into it at a constant rate
of 80 cm³s-¹
Find the rate at which the depth of water in the vase is increasing
a) when h=4

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Derivatives, Tangent Lines and Rates of Change are investigated. The solution is detailed and well presented.

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