# Stationary points - find horizontal line

• Jan 8th 2012, 05:03 AM
watp
Stationary points - find horizontal line
(I apologise if this is in the incorrect section)

I have a stationary points question that I really do not get. I have worked out that the SP's are (0,0) and (2,-4), but I do not know how to find Q.

Question:
Part of the graph of the curve with equation $\displaystyle y=3x^2-x^3$ is shown below.

Attachment 23205
(I used a graphic calculator online to draw the graph)

a) Establish the coordinates of the stationary point P.
b) The horizontal line through P meets the curve again at Q. Find the co-ordinates of Q.

So far, I have worked out the SPs:

$\displaystyle y=3x^2-x^3$
$\displaystyle \frac{dy}{dx}=6x-3x^2$
$\displaystyle -3(x-2)=0$
$\displaystyle -3x=0$ or $\displaystyle x-2=0$
$\displaystyle x=0$ or $\displaystyle x=2$

When x=0, y=0, point(0,0)
When x=2, $\displaystyle y=3(2)^2-3^3=4$ point(2,4) (which is P).

• Jan 8th 2012, 05:21 AM
Plato
Re: Stationary points - find horizontal line
Quote:

Originally Posted by watp
b) The horizontal line through P meets the curve again at Q. Find the co-ordinates of Q.
Solve $\displaystyle 4=3x^2-x^3$. That will give $\displaystyle (x,4)$
Solve $\displaystyle 4=3x^2-x^3$. That will give $\displaystyle (x,4)$