Title: Interpreting Derivatives PreVideo Questions
Course: Calculus I

Q: The images below show the graph of a logarithmic function given by y = f(x). To the right is an image zoomed in on the point (4 , f(4)). It turns out that  f `(4)= 0 . 17.
[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 4. (Incorrect)
- The length of the blue vector is f(4). (Incorrect)
- The length of the blue vector is 0.17. (Incorrect)
- The length of the blue vector is 0.17 times as much as the value of 4 (Incorrect)
- The length of the blue vector is 0.17 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 f(4). (Incorrect)
A: The length of the blue vector is 0.17 times as much as the value of ∆ x.

Q: The function b(t) gives the value of a particular baseball card in dollars where t is the number of years since the card was purchased. It turns out that b `(3)= 5. Which statement best explains the meaning of  b `(3)= 5.
- Three years after purchase, the card's value is $5. (Incorrect)
- Over the three years after it was purchased, the card's value increased by $5 every year. (Incorrect)
- Three years after purchase, the card's value will increase by $5 over the next year (Incorrect)
- As time increases by a very small amount from 3 years, the card's value increases by approximately 5 times as much as the change in time. (Correct)
- The instantaneous rate of change of the card's value with respect to time is 3. (Incorrect)
A: As time increases by a very small amount from 3 years, the card's value increases by approximately 5 times as much as the change in time.