Understand local linearity and formal definitions of the derivative

What is the primary purpose of finding a local line at any point on a graph?

• To find the slope at that point

• To identify the highest point on the graph

• To calculate the area under the graph

• To determine the color of the graph

What is a secant line?

• A line that is perpendicular to the Y-axis

• A line that is parallel to the X-axis

• A line that crosses the graph twice

• A line that touches the graph at one point

How is the slope of a secant line calculated?

• By dividing the difference in Y-values by the difference in X-values

• By multiplying the X-values

• By adding the Y-values

• By subtracting the X-values

What distinguishes a tangent line from a secant line?

• A tangent line touches the graph at only one point

• A tangent line is always horizontal

• A tangent line crosses the graph twice

• A tangent line is always vertical

What happens to the secant line as the distance between points decreases?

• It approaches the tangent line

• It becomes a vertical line

• It moves away from the tangent line

• It becomes a horizontal line

What is the role of limits in finding the tangent line?

• To decrease the distance between points

• To change the color of the graph

• To make the graph disappear

• To increase the distance between points

What value do we want the distance between points to approach to find the tangent line?

• One

• Zero

• Two

• Five