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

Q: The function goves the value of a particular baseball card in dollars where is the number of years since the card was purchased. It turns out that . Which statement best explains the meaning of .
- Three years after purchase, the card's value is $5.
- Over the three years after it was purchased, the card's value increased by $5 every year.
- Three years after purchase, the card's value will increase by $5 over the next year
- 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.
- The instantaneous rate of change of the card's value with respect to time 3 years after purchase is 5.
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.

Q: The images below show the graph of a logarithmic function given by . To the right is an image soomed 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 4.
- The length of the blue vector is .
- The length of the blue vector is 0.17.
- The length of the blue vector is 0.17 times as much as the value of 4
- 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 0.17 times as much as the value of .