Find the Tangent of y=1/(x-1) with Slope -1

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SUMMARY

The discussion focuses on finding the equation of the tangent line to the curve defined by y=1/(x-1) that has a slope of -1. The derivative of the function, y', is calculated to determine the point where the slope equals -1. By rewriting the function as y=(x-1)^-1, the derivative is found using the power rule, leading to the identification of the specific x-value where the tangent meets the slope condition.

PREREQUISITES
  • Understanding of calculus concepts, specifically derivatives
  • Familiarity with the power rule for differentiation
  • Knowledge of tangent lines and their equations
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Study the application of the power rule in calculus
  • Learn how to find tangent lines to various functions
  • Explore the concept of implicit differentiation
  • Investigate the behavior of rational functions and their derivatives
USEFUL FOR

Students studying calculus, mathematics educators, and anyone interested in understanding the principles of derivatives and tangent lines in relation to rational functions.

fiziksfun
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Find an equation for the tangent to the curve y=1/(x-1) that has slope -1.
 
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Ok you have y, you know that y'=-1. Is there a way you can find a point x where this happens?
 
If y= 1/(x-1)= (x-1)-1, what is y'? (I hereby give you permission to use (xn)'= nxn-1!)
 

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