Finding Slope of Tangent Line: How-To Guide

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SUMMARY

The discussion focuses on finding the slope of tangent lines for various segments of a piecewise linear function. Participants clarify that only straight lines possess a constant slope, while curves exhibit varying slopes at different points. The specific segments analyzed include three straight lines: from (-5, 5) to (-2, 2), from (-2, 2) to (0, 4), and from (0, 4) to (4, 2). The slope calculations for these segments are essential for understanding the concept of slope in both linear and non-linear contexts.

PREREQUISITES
  • Understanding of linear equations and slope calculation
  • Familiarity with piecewise functions
  • Basic knowledge of coordinate geometry
  • Ability to interpret graphical representations of functions
NEXT STEPS
  • Study the concept of slope in linear functions
  • Learn how to calculate slopes of piecewise linear functions
  • Explore the differences between tangent lines and secant lines
  • Investigate the application of derivatives in finding slopes of curves
USEFUL FOR

Students learning calculus, mathematics educators, and anyone interested in understanding the principles of slope in both linear and non-linear functions.

Teh
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My professor shown us in class how to find the slope but I still don't understand
 

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Find which slope? Surely your professor, when showing how to find slope explained that only straight lines have a single slope. Other curves, including "broken line curves" like this, have different slopes at different points. Here there are three different straight lines, one from (-5, 5) to (-2, 2), another from (-2, 2) to (0, 4), and the third from (0, 4) to (4, 2). What is the slope of each of those?
 

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