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## Homework Statement

Find all critical numbers of f(x)= x[tex]\sqrt{2x+1}[/tex]

## Homework Equations

Derivative, Product Rule

## The Attempt at a Solution

x[tex]\sqrt{2x+1}[/tex] = 0

x must be -1/2 & 0

(-1/2, 0) Critical Point.

(0, 0) Critical Point.

First derivative:

f'g + g'f

(1)([tex]\sqrt{2x+1}[/tex])+(1/2[tex]\sqrt{2x+1}[/tex])(x)(2)

=([tex]\sqrt{2x+1}[/tex]) + (x / [tex]\sqrt{2x+1}[/tex])

LCD:

(([tex]\sqrt{2x+1}[/tex]) ([tex]\sqrt{2x+1}[/tex]) + 1)) / ([tex]\sqrt{2x+1}[/tex])

= 2x+1 / [tex]\sqrt{2x+1}[/tex]

So y= 0 when x= -1/2 and 0

(-1/2, 0) Critical Point.

The second derivative I wouldn't post it her since it gets pretty messy. However, I found out that y=o for the second derivative must have x = -1/2

Now the problem is that my answer for all critical points are wrong. What am I doing wrong? PPLEASE HELP!