Both of your questions involve taking the first and second derivative of your function.

In (i), the first derivative is useful for finding critical points and seeing where the function is increasing or decreasing. The second derivative is used to see where the function is concave up or concave down. Your teacher should have reviewed a list of steps for drawing graphs this way.

In (ii), it is as it says, direct substitution. d^2s/dt^2 is the second derivative of s, ds/dt is the first derivative of s, and s is s. Plug in on the left hand side and see if it equals 0

done.