Derivative curve sketching (2 Viewers)

[atar90plus]

I was wondering if you guys could help me with these difficult questions. Could you guys please show the full working out and solutions.

Q1. Show that the following functions increase for all values of x in their domains

g) y=2x - 1/x

h) y=x + root 2x-1

Q2. Show that the following functions decrease for all values of x in their domains

b) y= -x^3+3x^2-4x+1

c) y=root 1-x

 

[deswa1]

<a href="http://www.codecogs.com/eqnedit.php?latex=\textup{Just take the derivative and prove its less than or greater than 0, depending on the question.}\\ \textup{For the first one...}\\ y=2x-\frac{1}{x}\\ \frac{dy}{dx}=2@plus;\frac{1}{x^2}\\ \frac{dy}{dx}\geq 2 \\\textup{ Therefore its increasing}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\textup{Just take the derivative and prove its less than or greater than 0, depending on the question.}\\ \textup{For the first one...}\\ y=2x-\frac{1}{x}\\ \frac{dy}{dx}=2+\frac{1}{x^2}\\ \frac{dy}{dx}\geq 2 \\\textup{ Therefore its increasing}" title="\textup{Just take the derivative and prove its less than or greater than 0, depending on the question.}\\ \textup{For the first one...}\\ y=2x-\frac{1}{x}\\ \frac{dy}{dx}=2+\frac{1}{x^2}\\ \frac{dy}{dx}\geq 2 \\\textup{ Therefore its increasing}" /></a>