What is the graph of the Cartesian equation $y = 0.75 x^{\frac{2}{3}} \pm \sqrt{1 - x^{2}}$ $y = 0.75 x^(2/3) +- sqrt(1 - x^2)$ ?

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Answer 1 · 2017-01-06T14:59:37

See the second graph. The first is for turning points, from y' = 0.

To make y real, $x \in [- 1, 1]$ $x in [-1, 1]$

If (x. y) is on the graph, so is (-x, y). So, the graph is symmetrical

about y-axis.

I have managed to find approximation tothe square of the two

higher-degree/zeros) of y' as 0.56, nearly.

So, the turning points are at $(\pm \sqrt{0.56}, 1.30) = (\pm 0.75, 1.30)$ $(+-sqrt 0.56, 1.30)=(+-0.75, 1.30)$ ,

nearly.

See the first ad hoc graph.

The second is for the given function.

graph{x^4+x^3-3x^2+3x-1 [0.55, 0.56, 0, .100]}
.
graph{(y-x^(2/3))^2+x^2-1=0 [-5, 5, -2.5, 2.5]}

What is the graph of the Cartesian equation y = 0.75 x^(2/3) +- sqrt(1 - x^2)y=0.75x23±√1−x2y = 0.75 x^(2/3) +- sqrt(1 - x^2)?