How do you Determine Increases/Decreases in a Function?

[Bosnrules]

How do you find out were the function increases/ decreases with the function: X^2-4 square root X.

here is what I have gotten so far:
y=x^2-4 square root X
dy/dx=2x-2^-(1/2)
dy/dx=1/(2x-2x^(1/2))



Thanx

 

[HallsofIvy]

$$y= x^2-4\sqrt{x}= x^2- 4x^{\frac{1}{2}}$$
$$y'= 2x- 2x^{-\frac{1}{2}}$$
(which I think is what you meant)
but I have no idea where you got that last formula. If you do write everything as a single fraction, you get
$$\frac{2(x^{\frac{3}{2}}-1)}{x^{\frac{1}{2}}}$$

Anyway, you want to first determine where the derivative is 0 or not defined.
$$x^{\frac{1}{2}}$$ is only defined for x> 0. Where is $$x- x^{-\frac{1}{2}= 0? Those points separate the positive real numbers into intervals. Determine on which intervals y' is positive or negative to determine in which intervals y is increasing or decreasing.$$

 

[ek]

I don't have any help for you, but how do you spell your own hometown wrong?

Drumheller.

For those who don't know, Drumheller is the home of the world famous Royal Tyrell Museum (Dinosaurs).