Chapter 3

Question 1

What are the two ways to analyze trends or slopes?

Answer 1

difference quotient
differential quotient

Question 2

What is the difference quotient?

Answer 2

used to determine the average slope between two points by using secant

Question 3

What is a curve

Answer 3

graph of nonlinear function
compromised of parabolas and hyperbola

Question 4

What is a secant?

Answer 4

line connecting two points
gives the rate of change

e.g.
f(x2)-f(x1)/x2-x1

Question 5

What is f(x) in an exponential called?

Answer 5

the production function

Question 6

What is the differential quotient

Answer 6

used to measure the slope of entire curve by using tangent
-also the limit function aka function slope aka derivative of function

Question 7

What is a tangent

Answer 7

line of contact at a point
just touches a point, doesn’t intersect with it and can be determined by using a slope triangle
it is the limit of the secant

Question 8

what does the limit formula mean?

Answer 8

when two points are close and they are hardly indistinguishable and the difference is a very small number it can be expressed by using limit.

Question 9

What does the △ triangle symbol in the limit formula mean?

Answer 9

the change

Question 10

What does lim mean?
△x->0

Answer 10

limit value of the change tends to be zero.