Courselo

Home
Learn
Practice(sign in to use)
Mock exams
Review(sign in to use)

Plan(sign in to use)
Progress(sign in to use)
Tutor(sign in to use)

Your plan

Save your progressA free account keeps your answers, predicts your score and builds a daily plan.Create a free account

Loading lesson

Loading your exam home

Home
Learn
Practice, sign in to use
Mocks
Review, sign in to use

Loading lesson

First-derivative analysis · AP Calculus AB · Courselo

Courselo

Calc AB
Learn
Unit 5: Analytical applications of differentiation

First-derivative analysis

Unit 5: Analytical applications of differentiation · Lesson 3 of 5

Lesson 3 of 5

Ask a tutor

Unit 5

Unit 5: Analytical applications of differentiation

5 lessons · 8 h 30 min of study

Extrema and critical points1 h 30 min of study
Mean Value Theorem and related results1 h 15 min of study
First-derivative analysisReading · 0%
Second-derivative analysis and curve sketching2 h of study
Optimization with derivatives2 h of study

This unit is ≈17% of the Calc AB, across 5 lessons. Full syllabus

Lesson 3 of 5 · Unit 5: Analytical applications of differentiation

First-derivative analysis

3 quick checks≈4% of the testCore: Core: tested on most papers

Reading is free. Sign in to tick off lessons, keep your place and track your mastery.

By the end you’ll be able to

Determine intervals where a function is increasing or decreasing.
Use sign changes in $f'(x)$ to identify local maxima and minima.
Apply the first derivative test.
Infer properties of $f$ from a graph or table of $f'(x)$.
Support conclusions with interval notation and concise justification.

Practice this skill

Adaptive questions on first-derivative analysis.

Practise this topic

0% read

This lesson hasn’t been written yet

Calc AB lessons are written from the official syllabus the first time a learner opens them, then saved for everyone. Sign in and this one is written for you in a minute or two. It’s free.

PreviousMean Value Theorem and related results Next lessonSecond-derivative analysis and curve sketching