ws17 - WORKSHEET 17 - Fall 1995 1. Find y both implicitly...

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WORKSHEET 17 - Fall 1995 1. Find y 0 both implicitly and explicitly for each relation below. a) x 1 / 2 + y 1 / 2 =1 b) | x | + | y | =1 c) x 2 + y 2 =1 d) x 3 + y 3 =1 2. Find y 0 for each of the parts of problem 1. 3. Consider the curve x 2 + y 2 - xy +3 x - 9=0. a) Find dy dx . b) Find two points on the curve where the tangent is parllel to the y -axis. 4. Let F ( u, v ) be a function of the two quantities u and v . Suppose also that u and v depend on another variable x . Then ultimately, F may be thought of as a function of x . Speci±cally, we may de±ne a function ˜ F ( x )by ˜ F ( x )= F ( u ( x ) ,v ( x )) . A generalized version of the chain rule applies here: d ˜ F dx = ∂F ∂u du dx + ∂F ∂v dv dx . Now suppose that we have de±ned y implicitly as a function of x by some equation F ( x, y )=0 . Use the above di²erentiatition rule to show that dy dx = - ∂F/∂x ∂F/∂y . (Hint: If
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ws17 - WORKSHEET 17 - Fall 1995 1. Find y both implicitly...

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