AP Calculus AB Analyzing Functions with Derivatives — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 8 definitions and 7 theorems, 5 worked examples, 6 diagrams, in 15 printable pages. This page lists what the notes cover. The notes themselves come with the AP Calculus AB bundle.
Unit notes — in the bundle
Not sold separately. The practice worksheet for this unit is free, with no email and no account.
Analyzing Functions with Derivatives — what the notes cover
11 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.
Also in this section: 1 note on method and common errors.
What you need
Also in this section: 1 note on method and common errors.
1. The Mean Value Theorem \hfill \normalsize\mdseries\itshape topic 5.1
- Theorem — The Mean Value Theorem
Also in this section: 1 worked example, 1 diagram.
2. Critical points \hfill \normalsize\mdseries\itshape topic 5.2
- Definition — Critical point
- Definition — Cusp and vertical tangent
Also in this section: 1 diagram.
3. What the sign of $f'$ says about $f$ \hfill \normalsize\mdseries\itshape topic 5.3
- Theorem — Increasing and decreasing functions
Also in this section: 1 diagram.
4. The First Derivative Test \hfill \normalsize\mdseries\itshape topic 5.4
- Definition — Relative (local) extremum
- Theorem — The First Derivative Test
Also in this section: 1 worked example, 1 diagram.
5. Absolute extrema on a closed interval \hfill \normalsize\mdseries\itshape topics 5.2, 5.5
- Definition — Absolute (global) extremum
- Theorem — The Extreme Value Theorem
- Theorem — The candidates test
Also in this section: 1 worked example.
6. Concavity and points of inflection \hfill \normalsize\mdseries\itshape topic 5.6
- Definition — Concave up and concave down
- Definition — Point of inflection
Also in this section: 1 diagram.
7. The Second Derivative Test \hfill \normalsize\mdseries\itshape topic 5.7
- Theorem — The Second Derivative Test
Also in this section: 1 note on method and common errors.
8. Connecting $f$, $f'$ and $f''$ \hfill \normalsize\mdseries\itshape topics 5.8--5.9
- Theorem — What the graph of says about
Also in this section: 1 diagram.
9. Optimization \hfill \normalsize\mdseries\itshape topics 5.10--5.11
- Definition — Objective function, constraint and feasible domain
Also in this section: 1 worked example, 1 note on method and common errors.
10. Implicit relations \hfill \normalsize\mdseries\itshape topic 5.12
- Definition — Horizontal and vertical tangents on an implicit relation
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 AP Calculus AB Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Analyzing Functions with Derivatives practice worksheet is free and stays free.
Every AP Calculus AB topic — the complete Solutions Bundle
One download, one payment, the whole program. For all 8 AP Calculus AB 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.
Analyzing Functions with Derivatives practice worksheet About the Analyzing Functions with Derivatives unit test