Link Derivative Implicit
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Communicating and Connecting What We Know About the Derivative of a Function
Symbolic
Graph
Given the relation:
xy + x – 2y – 1 = 0
Table x -3
y
Analysis dy/dx
1.
Determine the average rate of change of the function over the interval [1, 4].
-2 2. Graph dy/dx on the axes above.
-1 0
3. Determine the equation of the tangent line to the curve xy + x –2y – 1 at x = -1.
1 2 3 4
4. At what points, if any, are the tangents to the curve horizontal?
5. Determine the point(s) on the curve where the slope is .25.
Symbolic
Graph
Given the relation:
xy + x – 2y – 1 = 0
Table x -3
y
Analysis dy/dx
1.
Determine the average rate of change of the function over the interval [1, 4].
-2 2. Graph dy/dx on the axes above.
-1 0
3. Determine the equation of the tangent line to the curve xy + x –2y – 1 at x = -1.
1 2 3 4
4. At what points, if any, are the tangents to the curve horizontal?
5. Determine the point(s) on the curve where the slope is .25.
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