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Implicit Differentiation to Find Derivative

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Consider the curve xy^2 + y = 3 - x^2. Use implicit differentiation to find the derivative dy/dx

Hence determine the tangent to the curve at the point (-2,1)

A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 0.5ms-1. How rapidly is the area enclosed by the ripple increasing when the radius has become 5m?

Hint: This is a related rates question. A suggested start is to assign letters to all quantities that vary and then identify the known rates and the rate that is to be found.

Graph on the same axis:

1. y = 1/x

2. y = 1/x-3

3. y = 2 + (1/x-3)

Clearly label key points (eg. turning points, end points, discontinuities, etc if these exist).

Additionally, determine the domain and range for all four functions.

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