Represent y=x cube -x graphically.
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Trace the curve y=x3.
1. Domain, extent, intercept and origin; when x∈R, y is well defined.
As x→+∞; y→±∞, the curve exists in first and fourth quadrant only.
The intercepts with the axes are given by x=0, y=0 and when y=0, x=0
⇒ the curve passes through the origin.
2. Symmetry : By symmetry test, we have the curve is symmetric about origin.
3. Asymptotes : As x→+∞, y→+∞ and vice versa.
∴ the curve does not admit asymptotes.
4. Monotonicity : dxdy=3x2 , hence ∀x, dxdy>0
∴ the graph is monotonically increasing and will not intersect the axes at points other than origin.
5. dx2d2y=6x is 0 for x=0. Special point (0,0) is a point of inflection.
Step-by-step explanation:
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