Your formatting is ambiguous. I've broken the stream-of-consciousness math into separate lines, but I'm still confused.

The derivative, in the first pass, should have been as follows:

. . . . .[tex]A(x)\, =\, (a\, -\, x)\, 2\sqrt{\strut ax\,}[/tex]

. . . . .[tex]A'(x)\, =\, (-1)\,(2)\, \sqrt{\strut ax\,}\, +\, (a\, -\, x)\, (2)\, \dfrac{a}{2\, \sqrt{ax\,}}[/tex]

. . . . . . . . .[tex]=\, -2\, \sqrt{\strut ax\,}\, +\, \dfrac{2a\,(a\, -\, x)}{2\, \sqrt{ax\,}}[/tex]

Set this equal to zero. Solve the resulting linear

equation for x in terms of "a".

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