- #1
illegalvirus
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Homework Statement
Find the exact value of f''(2) if f(x)=[tex]\sqrt{3x-4}[/tex]
Homework Equations
See above
The Attempt at a Solution
I've tried to use the product rule to differentiate.
f= x(3x -4)[tex]^{\frac{1}{2}}[/tex]
f'= (3x -4)[tex]^{\frac{1}{2}}[/tex] + [tex]\frac{3}{2}[/tex][tex]^{\frac{-1}{2}}[/tex]
f''= [tex]\frac{3}{2}[/tex]x(3x -4)[tex]^{\frac{-1}{2}}[/tex] . [tex]\frac{3}{2}[/tex]x(3x -4)[tex]^{\frac{-1}{2}}[/tex] + (3x -4)[tex]^{\frac{1}{2}}[/tex] . [tex]\frac{-9}{4}[/tex]x(3x-4)[tex]^{\frac{-3}{2}}[/tex]
= [tex]\sqrt{3x -4}[/tex] . [tex]\frac{-9x}{4\sqrt{(3x-4)^{3}}}[/tex]
Now I am kind of stuck here. I've tried it a few times and I have no idea what I am doing wrong, some advice please?