University Business Math Curve Analysis and Business Optimization — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 7 definitions and 6 theorems, 6 worked examples, 2 diagrams, in 15 printable pages. This page lists what the notes cover. The notes themselves come with the University Business Math bundle.
Unit notes — in the bundle
Not sold separately. The practice worksheet for this unit is free, with no email and no account.
Curve Analysis and Business Optimization — what the notes cover
7 sections, in the order the unit is taught. Each entry below is the title of a definition or a theorem the notes state in full.
What you need
Also in this section: 1 note on method and common errors.
Critical numbers and the first derivative
- Definition — Critical number
- Theorem — Increasing, decreasing and the first-derivative test
Also in this section: 1 worked example, 1 note on method and common errors.
Concavity, inflection and diminishing returns
- Definition — Concavity and inflection points
- Theorem — The second-derivative test
- Definition — Point of diminishing returns
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Asymptotes and the shape of a rational curve
- Definition — Vertical and horizontal asymptotes
- Theorem — Asymptotes of a rational function
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Absolute extrema on an interval
- Definition — Absolute extrema
- Theorem — Finding the absolute extrema
Also in this section: 1 worked example, 1 note on method and common errors.
Maximizing revenue and profit
- Definition — Revenue, cost and profit
- Theorem — Maximum profit: marginal revenue equals marginal cost
Also in this section: 1 worked example, 1 note on method and common errors.
Minimizing cost and average cost
- Definition — Average cost
- Theorem — Minimum average cost: marginal cost equals average cost
Also in this section: 1 worked example, 1 note on method and common errors.
Where the notes are
The notes are one of the documents in the University Business Math Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Curve Analysis and Business Optimization practice worksheet is free and stays free.
Every University Business Math topic — the complete Solutions Bundle
One download, one payment, the whole program. For all 9 University Business Math units: the worksheet, the reference notes, the challenge set, the unit test and every answer key — these notes included.
- Worked solutions, not answer lists — every step written out
- Covers the whole year's program at this level
- Less than the price of one hour of tutoring — for the entire year's solutions
Practise it, then test yourself
Notes on their own do not make anything stick. This unit has a free, printable practice worksheet, and an end-of-unit test that comes with the bundle.
Curve Analysis and Business Optimization practice worksheet About the Curve Analysis and Business Optimization unit test