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Homework Statement
Find all critical numbers of f(x)= x\sqrt{2x+1}
Homework Equations
Derivative, Product Rule
The Attempt at a Solution
x\sqrt{2x+1} = 0
x must be -1/2 & 0
(-1/2, 0) Critical Point.
(0, 0) Critical Point.
First derivative:
f'g + g'f
(1)(\sqrt{2x+1})+(1/2\sqrt{2x+1})(x)(2)
=(\sqrt{2x+1}) + (x / \sqrt{2x+1})
LCD:
((\sqrt{2x+1}) (\sqrt{2x+1}) + 1)) / (\sqrt{2x+1})
= 2x+1 / \sqrt{2x+1}
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!