LEARN · EXPLAIN · REVISE

Find the increasing and decreasing intervals.

Read the idea, work independently, then explain what changed.

TOPIC 01

Derivatives and their applications: mixed review

A mixed assessment: identify the method, justify it and revise your reasoning.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Foundation#Your turn

f(x)=x^2-44x

A critical point needs a sign or second-derivative check; closed-interval global extrema also require endpoints.

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Differentiate the specified function and substitute only after differentiating.

Hint 2

Use this intermediate relation.

f\prime(x)=2(x-t)

Worked solution

Differentiate the specified function and substitute only after differentiating.
Apply the stated relation and retain its conditions.
$x<22:f'<0;\quad x>22:f'>0$
The derivative sign changes from negative to positive.

The requested relation or conclusion is shown below.

(-\infty,22):\searrow;\quad(22,\infty):\nearrow

Checks and common pitfalls: The derivative sign changes from negative to positive.

Reasoning checklist · self / teacher assessment

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment