On what interval(s) is the hummingbird moving to the right?

Question

The position of a hummingbird flying along a straight line is given by the functions(t)=(2t^3)/3−5t^2+8t−1 where t is measured in seconds and s is measured in yards. On what interval(s) is the hummingbird moving to the right?

Answer 1

The bird will be moving to the right when the derivative of s (which is the velocity) is positive.

Since the derivative is a quadratic, you can find the roots by factoring.

The parabola is positive on [0,1] and on [4,∞).

Note: a graph of the derivative will help you see this more clearly.