CramX
RegisterLog in
Back to AI Flashcard MakerMathematics /AP Calculus AB: 8.1.1 An Introduction to Curve Sketching

AP Calculus AB: 8.1.1 An Introduction to Curve Sketching

Mathematics7 CardsCreated 3 months ago

This set of flashcards introduces the use of derivatives for more precise curve sketching beyond basic algebraic graphing techniques. It covers key concepts such as identifying symmetry about the y-axis and origin, understanding how derivatives reveal the behavior of graphs, and ensuring smoothness without unexpected "wiggles."

PrintEmbedImportReport

Introduction to Curve Sketching

  • Applications of the derivative include motion problems, linear approximations, optimization, related rates, and curve sketching.

  • The techniques used in algebra for graphing functions do not demonstrate subtle behaviors of curves. You can use the derivative to describe the curvature of a graph more accurately.

Tap or swipe ↕ to flip
Swipe ←→Navigate
1/7

Key Terms

Term
Definition

Introduction to Curve Sketching

  • Applications of the derivative include motion problems, linear approximations, optimization, related rates, and curve sketching.

note

  • The derivative has many real-world applications,
    ranging from motion problems to related rates.

  • But the derivative is mor...

How can you tell if a graph is symmetric about the y‑axis?

If f(−x)=f(x), then the graph is symmetric about the y-axis.

How can you tell if a graph is symmetric about the origin?

If f (x) = − f (−x), then the graph is symmetric about the origin.

How can you tell that a curve doesn’t wiggle between plotted points?

By analyzing the slope as it changes.

Which of the following figures is not symmetric across both the origin and the y‑axis?

The line y = x

Log in to view all terms

Related Flashcard Decks

Mathematics

Essential SAT Math Formulas

This deck covers key formulas and concepts essential for the SAT Math section, including slope, distance, and vertex forms.

10 cards
View Deck
Mathematics

Algebra 1 Unit 1 Mastery Test

These properties of equality help maintain balance in an equation when performing the same operation on both sides. Inverse operations, like using addition to undo subtraction, are key tools in solving equations.

29 cards
View Deck
Mathematics

ATI TEAS Test Practice Mathematics Part 2

This flashcard set includes a variety of practical math questions covering percentages, conversions, averages, scale drawings, and basic algebra. It’s designed to strengthen problem-solving skills for real-life and standardized test situations.

53 cards
View Deck
Mathematics

ATI TEAS Test Practice Mathematics Part 1

This flashcard set includes a variety of practical math questions covering percentages, conversions, averages, scale drawings, and basic algebra. It’s designed to strengthen problem-solving skills for real-life and standardized test situations.

55 cards
View Deck
Mathematics

Unit 2 Progress Check: MCQ Part A

To determine the point where the tangent line to the graph of the function 𝑓f has a slope of 2 for 𝑥 >0 x>0, we use the fact that the slope of the tangent line at any point is given by the derivative 𝑓′(𝑥)f′(x).

15 cards
View Deck
Mathematics

Customary Liquid Measurement Units

This set of flashcards outlines key relationships between customary units of liquid measurement, including pints, cups, quarts, and gallons. It provides conversion facts to help understand how these units relate to one another in the U.S. measurement system.

3 cards
View Deck

Study Tips

  • Press F to enter focus mode for distraction-free studying
  • Review cards regularly to improve retention
  • Try to recall the answer before flipping the card
  • Share this deck with friends to study together
AP Calculus AB: 8.1.1 An Introduction to Curve Sketching
TermDefinition

Introduction to Curve Sketching

  • Applications of the derivative include motion problems, linear approximations, optimization, related rates, and curve sketching.

  • The techniques used in algebra for graphing functions do not demonstrate subtle behaviors of curves. You can use the derivative to describe the curvature of a graph more accurately.

note

  • The derivative has many real-world applications,
    ranging from motion problems to related rates.

  • But the derivative is more powerful still. You can
    use the derivative to more accurately sketch the
    graph of a function.

  • In algebra, you probably learned to sketch functions
    by plotting points. Then you connected the points
    together, assuming that they connected smoothly
    and without any wiggles.

  • However, you cannot be sure that graphs do not
    wiggle with the naïve approach used in algebra.
    Calculus will prove that the graph does not wiggle.

How can you tell if a graph is symmetric about the y‑axis?

If f(−x)=f(x), then the graph is symmetric about the y-axis.

How can you tell if a graph is symmetric about the origin?

If f (x) = − f (−x), then the graph is symmetric about the origin.

How can you tell that a curve doesn’t wiggle between plotted points?

By analyzing the slope as it changes.

Which of the following figures is not symmetric across both the origin and the y‑axis?

The line y = x

In which application is the derivative not used?

Calculating area under a curve