Question

The depth of a rain puddle D(t) is given in inches, and t is given in minutes. If the depth is changing with respect to time, which expression gives the rate of change at which the depth is changing at 1 minute? D″(1)D″(0) − D″(2)D′(1)D(0) − D(2)

Answer 1

The derivative evaluated at t=1 minute will give us the rate of change (or the slope) of the line equation which approximate the function at that point. In other words, the rate of change is given by

`m=(dD(t))/(dt)|_(t=1)=D^(\prime)(1)`

Therefore, the answer is option 3 from top to bottom.