Question

Write a structured and mathematically precise 4-6 sentence response to the following prompt:

Given a function, we can find its derivative, which describes how the function is changing.   Also if we are given a function that is describing how a quantity is changing, we can use its anti-derivative to determine exactly how much that quantity has changed.  

Recall the situation in a written assignment where you set a timer and start driving down the highway. Again suppose 'time 1' is 30 minutes of driving and 'time 2' is 1 hour 30 minutes of driving. Now suppose you have a device in your vehicle that records your odometer's reading (speed in miles per hour) at every time between time 1 and time 2. How could you determine the total distance traveled from this information? Would it be helpful if the device could output a graph of your speed vs time? How could formulate a mathematical expression involving antiderivatives to answer these questions?

Answer 1