I can't get any further down?
I don't know what I did wrong and would appreciate any help.
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How do you solve this problem without a calculator?
Until subtracting (which doesn’t keep you) everything was right (here it should be called +48 in front, because 0-(-48)=48).
Either you do it like Rammstein by dissolving equation II’ after, for example, a2 and using it in III’, or you reckon (complicated) 2*II’ – 3*III’: the a2 then falls away and you can calculate a1.
f(x) = ax^4 + bx^2 + c
f'(x) = 4ax^3 + 2bx
###
(1) f(0) = 0 –> c = 0
(2) f(3) = 0 –> 81a + 9b = 0
(3) f'(3) = -48 –> 108a + 6b = -48
(2) follows b = -9a
The compound used in (3) gives a=-8/9 and thus b=8
The last line would have to be +48.