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The equation x^2 y+2xy^3=8defines y as a function of x,y=f(x), near x=2, y=1. a) Find dy/dx. b) Now, find the slope of the curve x^2y+2xy^3=8 when x=2, y=1.

A rocket rises vertically from a point on the ground that is 100m from an observer at ground level. The observer notes that the angle of elevation is increasing at a rate of 12∘per second when the angle of elevation is 60∘. Find the speed of the rocket at...