Finding the Slope of Secant and Tangent Lines

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SUMMARY

The discussion focuses on calculating the slopes of secant and tangent lines for the parabola defined by the equation y = -x² + 2x - 1, specifically at the points P (2, -1) and Q (3, -4). The slope of the secant line PQ is determined using the formula (y2 - y1) / (x2 - x1), resulting in a slope of -3. The slope of the tangent line at point P is found using calculus, specifically by taking the derivative of the parabola, yielding a slope of 0. Finally, the equation of the tangent line at point P is derived as y = -1.

PREREQUISITES
  • Understanding of basic calculus concepts, particularly derivatives
  • Familiarity with the equation of a parabola
  • Knowledge of the slope formula for lines
  • Ability to perform basic algebraic manipulations
NEXT STEPS
  • Study the concept of derivatives in calculus to understand tangent lines better
  • Learn how to derive the equation of a line given a point and slope
  • Explore the properties of parabolas and their graphical representations
  • Practice calculating slopes of secant lines with different points on various curves
USEFUL FOR

Students learning calculus, particularly those focusing on the concepts of secant and tangent lines, as well as educators seeking to clarify these topics for their students.

cvc121
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Homework Statement


The points P (2,-1) and Q (3,-4) lie on the parabola y = -x2+2x-1
a) Find the slope of the secant line PQ.
b) Find the slope of the tangent line to the parabola to the parabola at P.
c) Find the equation of the tangent line at P.

Homework Equations

The Attempt at a Solution


I am just new to calculus and am having trouble determining the slope of a secant and tangent line. My attempt at the questions are attached. Can anyone verify my work to see if I am on the right track? Are my methods for solving for the slopes correct? Thanks! All help is very much appreciated!
 

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Yup. Looks good.
 
cvc121 said:

Homework Statement


The points P (2,-1) and Q (3,-4) lie on the parabola y = -x2+2x-1
a) Find the slope of the secant line PQ.
b) Find the slope of the tangent line to the parabola to the parabola at P.
c) Find the equation of the tangent line at P.

Homework Equations

The Attempt at a Solution


I am just new to calculus and am having trouble determining the slope of a secant and tangent line. My attempt at the questions are attached. Can anyone verify my work to see if I am on the right track? Are my methods for solving for the slopes correct? Thanks! All help is very much appreciated!
It looks fine.

20160226_203054-1-jpg.96503.jpg
 

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