2.9 Implicit Differentiation
1) Use implicit differentiation to find if x3 + y3 = 6xy.
2) Find if y3 + y2 – 5y – x2 = -4.
E) none of the above
3) Find the slope of the curve + = 9 at the point (1, 16).
4) Find the slope of the tangent line to the graph of x2 + 4y2 = 4 at the point (, – ).
5) Find an equation of the line tangent to the curve 2xy2 + x2y = 6 at the point (1, – 2).
A) 4x – 7y = 18
B) 4x + 7y = -10
C) 7x + 4y = -1
D) 7x – 4y = 15
E) none of the above
6) Find the slope of the curve tan(2x + y) = x at (0, 0).
7) If x sin y = cos (x + y), then calculate .
8) Find all points on the graph x2 + y2 = 4x + 4y at which the tangent line is horizontal.
A) (2, 2 – ) and (2, 2 + )
B) (1, 2 – ) and (2, 2 + )
C) (2, 2 – ) and (1, 2 + )
D) (0, 0) and (0, 4)
E) The tangent line is never horizontal.
9) Given the curve x3 + y3 = 9xy, find (a) the equation of its tangent line at the point (2, 4) and (b) the equation of its tangent line with slope -1.
10) Show that the curves given by y2 + 4y + 4x + 3 = 0 and y2 = 4x + 1 have a common tangent line and determine its equation.
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