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.© BrainMass Inc. brainmass.com June 20, 2018, 3:47 am ad1c9bdddf
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