What is the process for finding the stationary points of a curve?

[pip_beard]

Homework Statement

A curve is defined for x<-2 by the equation y=((x^2)+3)sqr(x+2)

a) Show that dy/dx=0 when x=-1 and find the x-coordinate of the other stationary point.

b) Find the value of d^2y/dx^2 when x=-1 hence determine whether the turning point is max or min.

Homework Equations

The Attempt at a Solution

y=((x^2)+3).(x+2)^1/2

Differentiate by product rule : u=x^2 +3 v=(x+2)^1/2
u'=2x v'=1/2((x+2)^1/2)

dy/dx= (x^2+3).0.5(x+2)^(-0.5) + (x+2)^0.5 . 2x

Where do i go from here>??

 

[pip_beard]

Then sub in -1 and i get dy/dx=0.. but how do i find the second stat point?>?

 

[Mentallic]

You need to solve dy/dx=0 like you would any other equation.
Substituting in x=-1 doesn't help you since you already know it's a stationary point so of course you'll get an answer of dy/dx=0 for x=-1.