# Prove the x-coordinate of this equation.

• April 28th 2009, 08:26 PM
MikeNZ
Prove the x-coordinate of this equation.
Not sure if you'd need a picture of the graph or not; don't think you would.

It just looks like an upside down parabola, but starts at 0 and cuts back through the x-axis.

The curve (C) has the equation

$y=3x^\frac{1}{2}-x^\frac{3}{2}$, $x\geq0$

The point A on C is a stationary point (is just a point at where the parabola turns back down [the tiny bit where it's flat]), and C cuts the x-axis at the point B.

Show that the x-coordinate of B is 3.

[I would of thought that if i substituted 3 into the above equation, y would equal 0?] it equals -9 however.

Find the coordinates of A.
• April 28th 2009, 08:39 PM
Calculus26
The derivative is 0 at a stationary point--in fact that's the definition
of stationary point