### Home > CALC > Chapter 5 > Lesson 5.2.1 > Problem5-54

5-54.

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

What does x and t stand for?

Refer to the hint in part (b).

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.

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