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Draw the rough sketch of the curve y=x^(...

Draw the rough sketch of the curve `y=x^(4)-x^(2)`.

Text Solution

Verified by Experts

We have `y=f(x)=x^(4)-x^(2)(x^(2)-1)=x^(2)(x-1)(x+1)`

`(x-1)rarr` graph crosses the x-axis at (1,0) without touching the x-axis.
`x^(2) rarr` Graph touches the x-axis at (0,0) and does not cross the x-axis.
`(x+1)rarr` Graph crosses the x-axis at (-1,0) without touching the x-axis.
Also function is even, hence the graph is symmetrical about the y-axis.
Hence the rough sketch of the curve is as shown in the following figure.
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