Rates of Change, Secants, and Tangents (3.1.1)

Question 1

• Approximate the instantaneous rate of change by finding the average rate of change on a small interval around the point in question.

Answer 1

• Approximate the instantaneous rate of change by finding the average rate of change on a small interval around the point in question.

Question 2

• Represent the average rate of change graphically by a secant line. The average rate of change is equal to the slope of the secant line between the two points being considered.

Answer 2

• Represent the average rate of change graphically by a secant line. The average rate of change is equal to the slope of the secant line between the two points being considered.

Question 3

• Represent the instantaneous rate of change graphically by a tangent line.

Answer 3

• Represent the instantaneous rate of change graphically by a tangent line.

Question 4

• To find the slope of a tangent line, take the limit of the function as the change in the independent variable approaches zero.

Answer 4

• To find the slope of a tangent line, take the limit of the function as the change in the independent variable approaches zero.