CPM Homework Help : CALC Problem 5-54

Hint (a):

Hint (b):

$\text{Recall that }\frac{dx}{dt} \text{ means }\lim_{\Delta t\rightarrow 0}\frac{\Delta x}{\Delta t}.$

What does x and t stand for?

Hint (c):

Refer to the hint in part (b).

Hint (d):

Analytic method: The ant will change directions when x'(t) changes sign.
Graphical method: The ant will change directions when the derivative graph CROSSES the x-axis.

Hint (e):

When velocity is positive, the ant is moving forward. When velocity is negative, the ant is moving backwards.