After completing the Ramp Lab in Chapter 2, Marquita decided to ride her bicycle down a nearby hill to gain more data on rolling objects. The data she collected is shown in the table below.
Can Marquita use this table to determine her exact velocity at
Tables only give us select values of a function. What values are we given that are close to
? Are these values close enough to find Marquita's exact velocity at ?
Approximate Marquita’s velocity at
using Hana’s method.
where represents the value whose slope you are looking for.
Note: Since we do note know values that are infinitely close to
, we can find Marquita's AROC (average velocity), not her IROC (actual velocity).
Marquita’s teacher observed that her data fits the function
. Assuming that her teacher is correct, compute Marquita’s exact velocities at and .
Use the Power Rule to find the IROC/derivative/slope function/velocity function. Then evaluate at
and again at .