find values of a,b,c and d such that $g(x)=ax^3+bx^2+cx+d$ has a local maximum at $(2,4)$ and a local minimum at (0,0)
2. Well you know $g(2)=4$ and $g(0)=0 \implies d = 0$
you can also use $g'(2)=g'(0)=0$