Part a.

The equation tells you the distance to the "certian fixed point". Therefore they are asking you if there is a solution to the equation:

Now if this can be solved then there will be values of t for which s(t) is negative. I suggest finding the values of t for which s(t) is maximum or minimum (the turning points). That is the point at which the derivative is equal to zero ( or )

Then when you know the value of t at the turning points substitute them into the equation for s(t) to find the extreme values of s(t). If they are all positive (or all negative) then the answer to their question is "no".

Part b.

The values that you found in part a define the boundaries between where s(t) is advancing and when it is retreating. You can tell if it is advancing or retreating from the value of s'(t). Unless I am mistaken a positive value means retreating.

Part c.

s``(t)= -12t + 42

When t > 42/12 s''(t) is negative (accellerating towards the certian fixed point).

When t< 42/12 s''(t) is positive (decellerating towards the fixed point.

I could have my signs back to frot in here so if you think I am wrong, then you may be right!