Worksheet 2.7 - Implicit Differentiation - Calculus Maximus Page 4
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7Calculus Maximus
WS 2.7: Implicit Differentiation
5. Consider the curve given by 6 + x
y = xy
3
2
2
2
dy
y
3
x y
(a) Show that
3
dx
x
2
xy
(b) Find every point(s) on the graph of the curve that has an x-coordinate of 1, then write an equation
for the tangent line at every/each of these point(s).
(c) The graph of the curve has vertical tangent lines. Find the x-coordinate of each of these vertical
tangent lines. Show the work that leads to your answer.
2
2
6. Find the two points where the curve
x
xy y
7
crosses the x-axis, and show that the tangents to
the curve at these points are parallel. What is the common slope of these tangents?
Page 4 of 7
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