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