I've zoomed in for you, and also plotted two more predictions from the model at time 30 and 31 seconds.

Clearly the maximum height is somewhere in here, because [code]g(29)=5111.65988[/code] and [code]g(31)=5116.34705[/code] are both a few meters lower than [code]g(30)=5118.92853[/code]. [br][br]Notice also, that the slopes between these points go from positive to negative. Specifically, the slope between the points [code](29,5111.65988)[/code] and [code](30,5118.92853)[/code] is positive:[br][br][math]\frac{\left(5118.92853-5111.65988\right)meters}{\left(30-29\right)seconds}\approx7.26865\frac{meters}{second}[/math][br][br]On the other hand, the slope between the points[code] (30,5118.92853)[/code] and [code](31,5116.34705)[/code] is negative:[br][br][math]\frac{\left(5116.34705-5118.92853\right)meters}{\left(31-30\right)seconds}\approx-2.58148\frac{meters}{second}[/math][br][br]So this means the rate of change of the height of the missile changed from increasing to decreasing somewhere in here as well -- a sure sign that a maximum height has occurred.[br][br]But is the maximum exactly [code]g(30)=5118.92853[/code] meters? Or does the maximum occur at a different time value? Try a few more guesses to see if you can find it! You can use decimals for inputs as well![br][br]Don't worry too much about this question though. We'll return to this later, and see that calculus is the perfect tool for doing this calculation without guessing.[br][br]Move forward whenever you're ready. We won't figure this out exactly just yet, but rest assured we'll take another look at this later in the book.