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

5-54.

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.