sketching y^2 = X^3

[aurao2003]

1. The problem statement, all variables and given/known data


Hi everyone, I am not sure how to sketch this:
y^2 = X^3
I have a feeling it will form a parabola.

If I find the square root of both sides I get:
y = X^3/2
Differentiating gives me
dy/dx = 1.5X^1/2. Kind of stuck from here. Please help.

2. Relevant equations



3. The attempt at a solution

[Mentallic]

Think about the shape of the graph for y=x2, then y=x3, y=x4 etc. only for values x>0. The shape is roughly the same, no? The only difference is that for x>1 the graph is steeper and for 0<x<1 the graph is lower for larger powers.
So y=x3/2 will be roughly the same as y=x2 for x>0
But remember that when you take the square root of both sides, you need to remember that \pm so your final result of y^2=x^3 or y=\pm x^{3/2} is the graph of y=x3/2 for values of x>0 and then exactly the same thing but reflected in the x-axis for y=-x3/2.

[Mark44]

1. The problem statement, all variables and given/known data


Hi everyone, I am not sure how to sketch this:
y^2 = X^3
I have a feeling it will form a parabola.

If I find the square root of both sides I get:
y = X^3/2
Actually, it's
y = \pm x^{3/2}
There are two branches.

Differentiating gives me
dy/dx = 1.5X^1/2. Kind of stuck from here. Please help.
The derivative also has two branches.
dy/dx = \pm 1.5x^{1/2}



2. Relevant equations



3. The attempt at a solution