Two More Predictions
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
g(29)=5111.65988 and g(31)=5116.34705 are both a few meters lower than g(30)=5118.92853.
Notice also, that the slopes between these points go from positive to negative. Specifically, the slope between the points (29,5111.65988) and (30,5118.92853) is positive:
On the other hand, the slope between the points (30,5118.92853) and (31,5116.34705) is negative:
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.
But is the maximum exactly g(30)=5118.92853 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!
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.
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.