Where did I do this min/max problem incorrectly? Current price of a car is \$20,000 The current price changes at a rate of $50-50\sqrt{t}$ When will the price of a new car be at a maximum? So.... $$\frac{dp}{dt}=p'(t)=50-50\sqrt{t}$$ First, to determine where there is a min/max, I set $f'(x)=0$ _(I would then do 2nd deriv. test to determine if its a min or max)_ $$50-50\sqrt{t}=0$$ $$50=50\sqrt{t}$$ $$1=\sqrt{t}$$ $$1=t$$ However, t=1 is not a choice. What have I done wrong?

You are doing fine. For $t \lt 1$ the rate of change is positive, for $t \gt 1$ the rate of change is negative, so $t=1$ is the maximum.