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Tangent Lines and Rates of Change

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Calculus and Analytical Geometry
MTH101
LECTUER ­ 14
Tangent Lines and Rates of
Change
Slope of a Tangent Line
If a secant line is drawn between
two points P and Q on a curve, then
the slope of this secant line is
If we let X1 approach XD  , then Q will
approach P along the graph of f, and the
secant line through P and Q will approach
the tangent line at P. Thus slope of secant
approaches the slope of tangent.
Mth101
Page 43
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Calculus and Analytical Geometry
Tangent Lines and Rates of
Change
This shows that secant line approaches to
tangent line. Thus we can conclude that the
slope of this tangent line is the instantaneous
velocity.
Mth101
Page 44
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Calculus and Analytical Geometry
Tangent Lines and Rates of
Change
Example
Solution
Mth101
Page 45
Table of Contents:
  1. Coordinates, Graphs and Lines
  2. Absolute Values
  3. Coordinate Planes and Graphs
  4. Line and Definition of Slope
  5. Distance, Circles, Quadratic Equations
  6. Functions and Limits
  7. Operations on Functions
  8. Graphs of Functions
  9. Limits (Intuitive Introduction)
  10. Limits and Computational Approach
  11. Limits: A Rigorous Approach
  12. Continuity
  13. Limit and Continuity of Trigonometric Functions
  14. Tangent Lines and Rates of Change
  15. The Derivative