To find:The slopes of tangents to the given relations at given points.
Answer to Problem 38E
The slopes of tangents at given points are given in table below:
x | slope |
-0.5 | - 1 |
+0.5 | - 1 |
-1 | +8 |
+1 | - 8 |
0 | undefined |
The graph of the curve is shown in figure.
Explanation of Solution
Given information:
The given implicit relation is
Method/Formulaused:
The slope of tangent line ( m ) at point
Calculations:
The given relation that represents a curve is
Differentiating with respect to ‘ x’
Now, from relation (1)
Now, for
Hence, the slope of tangent at
Now, for
Hence, the slope of tangent at
Now, for
Hence, the slope of tangent at
Now, for
Hence, the slope of tangent at
Now, for
Hence, the slope of tangent at
that is undefined.
The graph of the curve and tangents at given points are shown in figure here.
Conclusion:
The slopes of tangents at given points are given in table below:
x | slope |
-0.5 | - 1 |
+0.5 | - 1 |
-1 | +8 |
+1 | - 8 |
0 | undefined |
The graph of the curve is shown in figure.
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