Hi

We know two things :

- That x=2 is a stationary point hence f'(2)=0. This equation can be solved for k.

- That f(2)=1. As f'(x)=16x+k, integrating you get f(x)=... + constant and the equation f(2)=1 will give you the value of the constant.

Then simply compute f(7) and you are done.