Week 10 Study Guide — Applications of Differentiation

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Directly supported by notes

These three sub-topics are explicitly named in the workshop exercise PDFs:

Topic	Direct source coverage
Critical points	First and second derivative tests; 10 worked exercises
Optimization	Geometric, cost, and distance scenarios; 10 worked exercises
Related rates of change	Chain-rule rate problems; 3 worked exercises

The workshop expects you to be able to:

Compute $f^{'} (x)$ and $f^{''} (x)$ cleanly for polynomial, exponential, logarithmic, trig, and rational functions.
Set up and reduce a constrained word problem to a one-variable function.
Differentiate both sides of a geometric relationship with respect to time.

The lecture (PDF only partially readable) almost certainly covers, in this order:

Definition of a critical point.
The first derivative (sign-change) test, with a worked example.
The second derivative (concavity) test, with a worked example.
A statement of when the second derivative test is inconclusive and you fall back to the first.
One or two optimisation worked examples (rectangle area, cost minimisation).
The chain rule re-stated for related rates, with the classic “ladder against a wall” or balloon example.

May appear in the lecture but is not in the workshop PDFs:

Extreme Value Theorem on a closed interval (continuous functions attain max + min).
Mean Value Theorem.
Concavity and inflection points more formally.

The lecture PDF (EGD105 - Lecture Week 10 - post.pdf) did not parse cleanly here — verify the worked examples in your own copy of the slides.
Whether the assessment focuses on classification (min/max/neither) or also asks about inflection points.

Two notes cover the topic at different depths:

Cheatsheet — every rule, table, and recipe in one page. Includes the full quiz (mixed difficulty, reshuffles every visit).
In-depth analysis — why each technique works, the Taylor-series argument behind the second derivative test, the chain rule’s connection to related rates, and a full exam-style worked example.

Plugging numeric values in before differentiating in related-rates problems.
Treating $f^{''} (c) = 0$ as conclusive (it isn’t — it’s “inconclusive, fall back to the first-derivative test”).
Setting up an optimisation problem in two variables and trying to differentiate before using the constraint.
Forgetting the endpoints when optimising on a closed interval.
Dropping the sign (and the units) in the final answer.

Pick any from the workshop PDFs. Recommended for a first pass:

Optimization and related rates almost always appear on the exam paper. Critical-point classification underpins both.

Directly supported: the three workshop topics, their problems, and their answers.
Inferred: the lecture’s framing and order.
Gap: lecture slide content beyond what the workshop questions imply.