Distance: $\displaystyle s=-16t^2+800t$

find t, for s increasing, for s'=0, and for s decreasing

Am I figuring maximums and minimums here?

$\displaystyle y'=-32t+800$ =$\displaystyle y'=-t+25$

so I have a critical point at x=25

$\displaystyle y''=-1$

So our singular critical point is a maximum. So t>25 we start to decrease?

I have a multiple choice solution set

a.) (0,25]

increasing

{0,50}

s=0

b.)[25,50]

decreasing

{0,50}

s=0

c.) {0,50}

s=0

d.) None of these

Keep in mind. He likes to trick us and I've noticed a lot of "none of these" resulting from things like positive and negative signs in the equation. Part of the thing confusing me is how he wrote up the solution set