Homework Help: Math 31 Curve Sketching Help!

1. May 10, 2005

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

Last edited: May 10, 2005
2. May 10, 2005

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 [tex]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.

3. May 11, 2005

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).