Calculus: Tangents and Normals

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Questions and Answers

Yatay bir teğet çizgisi, lokal bir maksimum veya minimum göstergesidir.

True (A)

Türev, bir eğrinin grafiğinin bir noktadaki normal çizgisinin eğimini sağlar.

False (B)

Üçgende hangi özelliğe göre üçgende bir açı 180°'den küçüktür?

  • Dış açılardan biri
  • İç açılardan ikisi
  • İç açılardan biri (correct)
  • Tüm iç açılardan biri

Küre dikdörtgen olarak adlandırılır, çünkü tüm kenarları eşit uzunluktadır ve tüm köşeleri dik açılardır.

<p>Kare (B)</p> Signup and view all the answers

Çevre uzunluğu, hangi şeklin etrafında bulunan uzunluktur?

<p>Çember (B)</p> Signup and view all the answers

Hangi tür üçgende tüm kenarlar eşit uzunluktadır?

<p>Eşkenar üçgen (D)</p> Signup and view all the answers

Dikdörtgenin alan formülü nedir?

<p>A = l × w (B)</p> Signup and view all the answers

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Study Notes

Tangents And Normals

Tangent Lines

  • A tangent line to a curve at a point is a line that just touches the curve at that point.
  • The slope of the tangent line represents the instantaneous rate of change of the function at that point.
  • The derivative of a function at a point gives the slope of the tangent line at that point.

Normal Lines

  • A normal line to a curve at a point is a line that is perpendicular to the tangent line at that point.
  • The normal line passes through the point of tangency and is perpendicular to the tangent line.
  • The slope of the normal line is the negative reciprocal of the slope of the tangent line.

Geometric Interpretation

  • The derivative of a function can be interpreted as the slope of the tangent line to the graph of the function.
  • The tangent line is a good approximation of the function near the point of tangency.
  • The normal line is perpendicular to the tangent line and passes through the point of tangency.

Visualizing Derivatives

  • The derivative can be visualized as the slope of the tangent line to the graph of the function.
  • The steeper the tangent line, the larger the derivative.
  • A horizontal tangent line indicates a local maximum or minimum.

Key Points

  • The derivative gives the slope of the tangent line to the graph of the function.
  • The tangent line and normal line are perpendicular to each other.
  • The derivative can be visualized as the slope of the tangent line.

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