Find constants a and b such that the graph of f(x)=x³+ax²+bx will have a local max at (-2,9) and a local min at (1, 7).

Stationary point when f'(x)=0

 

Its a max if  f"(x)<0  and its a min if   f"(x)>0

 

so you are expected to differentiate and plug in the points.