Assignment:
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.
Provide complete and step by step solution for the question and show calculations and use formulas.