### In the Beginning - Chapter 3

*Previously, we had an incredible road trip and figured out the rates of velocities we have traveled...*

*and then...*

*we went backwards.*

*Now we needed to solve the distance for a specific velocity.*

*How did we do it?*

*Here's how:*If in the previous chapter, we spent hours and hours on calculating velocities, slopes or derivatives, this time the

**DISTANCE**is what we will sweat on. It is like reversing the solutions we have done in Chapter 2.

Basically, to acquire the distance, we use the formula:

**DISTANCE = VELOCITY * TIME ELAPSED**

Obtaining the precise distance is not as easy as multiplying the velocity by the time elapsed, since in a typical graph, the

*velocity is changing moment by moment*. So to have better measure,

**. These estimates are the slowest and largest estimates of the graph, respectively. But having those won't make it any closer to an accurate distance.**

*a LOWER ESTIMATE and an UPPER ESTIMATE must be considered***SMALLER INTERVALS must be used.**At a particular point,

*its LEFT-HAND SIDE and RIGHT-HAND SIDE are to be added and divided into half.*In solving, it is better to first look at how the graph behaves. It is easier to get the distance of a point in a graph that looks like a line - a linear function. This graph is called

**MONOTONIC**since it can only be

**. But sometimes,**

*STRICTLY INCREASING or STRICTLY DECREASING***NON-MONOTONIC graphs can be turned into MONOTONIC**.

In an INCREASING GRAPH, the LEFT-HAND side is the LOWER ESTIMATE and the RIGHT-HAND side is the UPPER ESTIMATE. In a DECREASING GRAPH, the LEFT-HAND side is the UPPER ESTIMATE and the RIGHT-HAND side is the LOWER ESTIMATE.

... There you go. My own summary of what I learned in the first discussion of

*CALCULATING THE DISTANCE TRAVELED.*and... as planned, Prince is the next scribe. (^_^)

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