Title: Interpreting Derivatives Post-Video Questions
Course: Calculus Videos Project > Section: Interpreting Derivatives

Q: Water is vlowing into a tank. The function gives the depth of the water in meters when the volume of the water in the tank is cubic meters. It turns out that . Which statement best explains the meaning of .
- When the volume is 10 cubic meters, the depth is 2 meters.
- As the volume increased from 0 to 10 cubic meters, the depth increased by 2 meters for every cubic meter of water.
- When the volume is 10 cubic meters, the depth will increase by 2 meters.
- As volume varies by a very small amount from 10 cubic meters, the depth of the water increases by 2 times as much as the change in volume.
- The instantaneous rate of change of the depth's value with respect to volume when the volume is 10 cubic meters is 2 meters per cubic meter.
A: As volume varies by a very small amount from 10 cubic meters, the depth of the water increases by 2 times as much as the change in volume.

Q: The images below show the graph of a parabola given by . To the right is an image zoomed in on the point . It turns out that .

After zooming enough to where the graph of appears especially linear, which statement best describes the length of the blue vertical vector?
- The length of the blue vector is 0.75.
- The length of the blue vector is 3.
- The length of the blue vector is .
- The length of the blue vector is 0.75 times as much as the value of
- The length of the blue vector is 0.17 times as much as the value of .
- The length of the blue vector is 0.17 times as much as the value of .
A: The length of the blue vector is 0.75 times as much as the value of