I assume that the graph of f is continuous and once (but only once!) differentiable - even though that isn't stated in your problem, but otherwise you can't calculate the missing values.

Divide the graph of f' into 4 parts concerning the intervals [0,1), [1, 3), [3, 5) and [5, 6]:

to [0, 1): Thegraph of fis a parabola whose quadratic term is . Therefore :....

to [1, 3): Thegraph of fis a straight line whose linear term is . Therefore :....

to [3, 5): Thegraph of fis a parabola whose quadratic term is . Therefore :....

to [5, 6]: Thegraph of fis a straight line whose linear term is . Therefore :....