Title: Interpreting Derivatives PostVideo Questions
Course: Calculus I

Q: The images below show the graph of a parabola given by y = f(x). To the right is an image zoomed in on the point (3 , f(3)). It turns out that f `(3)= 0 . 75.
[Image: PIC]
After zooming enough to where the graph of f 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 f(3). (Incorrect)
- The length of the blue vector is 0.75 times as much as the value of ∆ x. (Correct)
- The length of the blue vector is 0.17 times as much as the value of 3. (Incorrect)
- The length of the blue vector is 0.17 times as much as the value of f(3). (Incorrect)
A: The length of the blue vector is 0.75 times as much as the value of ∆ x.

Q: Water is vlowing into a tank. The function d(v) gives the depth of the water in meters when the volume of the water in the tank is v cubic meters. It turns out that d `(10)= 2. Which statement best explains the meaning of  d `(10)= 2.
- 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 approximately 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. (Incorrect)
A: As volume varies by a very small amount from 10 cubic meters, the depth of the water increases approximately by 2 times as much as the change in volume.