Math 1200 Learning Guide Flashcards - Blocks 1, 2, and Multiple Choice Section 1

Vocabulary flashcards covering Economic Functions, Extrema, Rates of Change, Lines, and Derivatives based on Math 1200 learning guides.

Block 1: Economic Functions Assessment

A content block counting for $7\%$ of the final grade in Math 1200, assessed during Midterm 1 and the final exam with the higher score counting.

Cost Function

A mathematical function representing total production cost, consisting of fixed costs and variable costs for items produced.

Fixed Cost

Production costs that remain constant regardless of the quantity of items produced.

Variable Cost

Production costs that vary depending on the quantity of items produced or components used.

Revenue Function

A function calculating total income generated from selling a specific quantity of items, determined by a fixed selling price or a demand equation.

Profit Function

A function calculated as total revenue minus total cost ($\text{Profit} = \text{Revenue} - \text{Cost}$).

Break-even Point

The production or sales level where total revenue equals total cost, or where profit equals zero.

Supply Function

A mathematical relationship indicating the quantity supplied at a given price or the price corresponding to a given quantity supplied.

Demand Function

A mathematical relationship indicating the quantity demanded at a given price or the price corresponding to a given quantity demanded.

Equilibrium

The specific price and quantity combination where the supply function equals the demand function.

Block 2: Extrema Assessment

A content block counting for $7\%$ of the final grade in Math 1200, with two assessment opportunities (Midterm 1 and the final exam).

Derivative Sign Chart

A tool constructed using the derivative of a function to determine intervals where the function is increasing or decreasing.

Stationary Point

A point on a function consisting of an x-value and a y-value where the derivative is equal to zero ($f'(x) = 0$).

Singular Point

A point on a function consisting of an x-value and a y-value where the derivative does not exist or is undefined.

Endpoint

A boundary point determined by the domain of a function, defined by an x-value and a y-value computed using the original function.

Relative (Local) Extrema

Local maximum or minimum points of a function occurring where the derivative changes sign, or at endpoints.

Absolute Extrema

The maximum or minimum values of a function over its entire domain, found by comparing y-values at stationary points, singular points, and endpoints.

Multiple Choice Section 1

An assessment counting for $5\%$ of the final grade, covering course material from day 1 week 1 through day 1 week 5.

Average Rate of Change

The change in function value divided by the change in the input variable over a specified interval.

Instantaneous Rate of Change

The rate of change of a function at a specific point, evaluated using its derivative.

Tangent Line

A straight line touching a function at a given x-value, with a slope equal to the derivative of the function evaluated at that x-value.