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Slope and Equation of Normal & Tangent Line of Curve at Given Point - Calculus Function & Graphs
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- Опубліковано 4 вер 2016
- This calculus video shows you how to find the slope and the equation of the tangent line and normal line to the curve/function at a given point. This video contains plenty of example problems.
Derivatives - Fast Review: • Calculus 1 - Derivatives
Equation of the Tangent Line:
• How To Find The Equati...
Derivatives - Horizontal Tangent Line:
• How to Find The Point ...
The Equation of The Normal Line:
• How To Find The Equati...
The Equation of The Secant Line:
• How To Find The Equati...
_________________________________
Average and Instantaneous Velocity:
• Average Velocity and I...
Instantaneous Rate of Change:
• Instantaneous Rate of ...
Derivatives of Rational Functions:
• Derivatives of Rationa...
Derivatives of Radical Functions:
• Derivatives of Radical...
Derivatives of Fractions:
• How To Find The Deriva...
________________________________
Derivatives - Higher Order:
• Higher Order Derivatives
Simplifying Derivatives:
• Simplifying Derivatives
Derivatives - The Product Rule:
• Product Rule For Deriv...
Derivatives - The Quotient Rule:
• Quotient Rule For Deri...
Derivatives - The Chain Rule:
• Chain Rule For Finding...
_______________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
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Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
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The video explains how to find the slope and equation of the tangent line at a given point using derivatives and limits in calculus. It covers finding derivatives of functions, calculating slopes, and writing equations of tangent and normal lines. Examples and visualizations are provided to aid understanding.
Key moments:
00:01 Learn to find the slope of the tangent line at a point using derivatives and the equation of the tangent line. Understand the importance of derivatives and limits in calculus.
-Understanding derivatives and their application in finding slopes of tangent lines. Derivatives of monomials and constants. Derivative of a constant is always zero.
-Finding the slope of the tangent line at a specific point. Using the derivative function to calculate the slope. Determining the equation of the tangent line using the slope and a point.
06:31 Understanding derivatives as functions and using limits to find the slope of a tangent line are crucial in calculus. Simplifying expressions through limits helps determine the slope of the tangent line accurately.
-Derivatives as functions and using limits to find the slope of a tangent line are fundamental concepts in calculus.
-Demonstrating how to find the equation of a tangent line and simplify expressions to determine the slope of the tangent line accurately.
14:04 Factoring an expression involves identifying the GCF and applying the difference of squares method. Finding the slope of a tangent line can be done using limits or the average rate of change.
-Factoring involves identifying the GCF and applying the difference of squares method to simplify expressions.
-Finding the slope of a tangent line can be achieved using limits by substituting values and calculating the derivative.
20:43 The average rate of change approaches the instantaneous rate of change as the difference between two points decreases, resulting in the secant line's slope closely resembling the tangent line's slope.
-Understanding how the average rate of change converges to the instantaneous rate of change as the difference between two points decreases.
-Calculating the slope of the tangent line using the average rate of change and its approximation to the instantaneous rate of change.
27:56 To find the equation of the normal line, replace the slope with its reciprocal and solve for the y-intercept. The slope of the tangent line can be found by evaluating the derivative at a given point.
-Calculating the slope of the normal line involves replacing the slope with its reciprocal and solving for the y-intercept using the given point.
-To find the slope of the tangent line at a specific point, evaluate the derivative of the function at that point to determine the slope.
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How do you distinguish when to place a 2 or 1 when trying to find the slope of a tangent line when plugging it back into the inverse equation?
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