At t = 0 the height is 8 and the length is 10. The length is decreasing at the rate of 1/4 of an inch per second while the height is increasing at the rate of half an inch per second. Is there a maximum possible area for the rectangle and if so when does it occur.
Just remembered how to do this. If we plot the area polynomial over time we get a parabola and we want to know when the parabola rate of change is zero, because that's when the parabola is at its max.
Therefore we take the derivative and set it equal to zero.