Title: Interpreting Derivatives PostVideo Questions
Course: Calculus Videos Project Modules

Q: The images below show the graph of a parabola given by [Image: equation]. To the right is an image zoomed in on the point [Image: equation]. It turns out that [Image: equation].
[Image: image]
After zooming enough to where the graph of [Image: equation] appears especially linear, which statement best describes the length of the blue vertical vector?
- The length of the blue vector is 0.75. (Incorrect)
- The length of the blue vector is 3. (Incorrect)
- The length of the blue vector is [Image: equation]. (Incorrect)
- The length of the blue vector is 0.75 times as much as the value of [Image: equation] (Correct)
- The length of the blue vector is 0.17 times as much as the value of [Image: equation]. (Incorrect)
- The length of the blue vector is 0.17 times as much as the value of [Image: equation]. (Incorrect)
A: The length of the blue vector is 0.75 times as much as the value of [Image: equation]

Q: Water is vlowing into a tank. The function [Image: equation] gives the depth of the water in meters when the volume of the water in the tank is [Image: equation] cubic meters. It turns out that [Image: equation]. Which statement best explains the meaning of [Image: equation].
- When the volume is 10 cubic meters, the depth is 2 meters. (Incorrect)
- As the volume increased from 0 to 10 cubic meters, the depth increased by 2 meters for every cubic meter of water. (Incorrect)
- When the volume is 10 cubic meters, the depth will increase by 2 meters. (Incorrect)
- 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. (Correct)
- 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. (Incorrect)
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.