Question

I need help,
How to find out the polynomial f(x) such that f(1) =f(-1)=f(0) =0 and f'(1) =f'(-1)=f'(0) =0 also
Please, help

Answer 1

I know with those 3 roots, f(x) = x (x^2 -1) *(.....)
with those f', I need (-1,f(-1)), (0,f(0)) , (1,f(1) ) are all minimum or maximum
but get stuck