Graphing and Finding Tangent Lines of Quadratic Functions - Derivatives Help

Click For Summary
SUMMARY

The discussion focuses on sketching the graphs of the quadratic functions y = x² and y = -x² + 6x - 5, and finding the equations of the tangent lines to both graphs. The user, Paul, has successfully graphed the parabolas and calculated their derivatives, but seeks confirmation on his approach. The conversation emphasizes the importance of identifying the points of tangency, labeled as Xsub1 and Xsub2, to derive the correct tangent line equations.

PREREQUISITES
  • Understanding of quadratic functions and their graphs
  • Knowledge of derivatives and their application in finding slopes
  • Familiarity with the concept of tangent lines in calculus
  • Ability to sketch and analyze parabolic equations
NEXT STEPS
  • Study the process of finding derivatives of polynomial functions
  • Learn how to determine points of tangency for curves
  • Explore methods for sketching graphs of quadratic functions
  • Investigate the application of tangent line equations in real-world scenarios
USEFUL FOR

Students studying calculus, mathematics educators, and anyone interested in understanding the graphical representation of quadratic functions and their derivatives.

Aspekt
Messages
4
Reaction score
0
I was having some trouble with a problem. The problem reads:
Sketch the graphs of y = x^2 and y = -x^2+6x-5, and sketch the two lines that are tangent to both graphs. Find equations of these lines.

I've graphed the two parabolas and drew the tangent lines. I've found the derivatives of each equation as well. I relabeled the points where the tangent line is tangent on each of the parabolas using Xsub1 and Xsub2. Am I going about doing this the correct way? Can someone give me a little help, thanks.

-Paul
 

Attachments

  • 73.JPG
    73.JPG
    8.8 KB · Views: 446
Physics news on Phys.org
What you are saying you are doing is correct. Since haven't actuall shown what you did, I can't say whether you are doing it correctly.
 
anyone can help me with that problem ? i dunt know how to do it !
 

Similar threads

Solving Tangent Lines for 2 Graphs: x1,x2
  • · Replies 6 ·
Replies
6
Views
3K
Quadratics Having a Common Tangent
  • · Replies 1 ·
Replies
1
Views
1K
Can a Function Have Two Different Tangent Lines at the Same Point?
  • · Replies 2 ·
Replies
2
Views
2K
Find the equation of a tangent line to y = x^2?
  • · Replies 11 ·
Replies
11
Views
5K
Find eqn for "normal" line to the tangent- folium
  • · Replies 6 ·
Replies
6
Views
2K
Show plane curve can be described with graph @ tangent point
  • · Replies 6 ·
Replies
6
Views
2K
Finding the horizontal tan() lines of this equation
  • · Replies 3 ·
Replies
3
Views
2K
Finding the Slope of Secant and Tangent Lines
  • · Replies 2 ·
Replies
2
Views
3K
Show that this graph isn't differentiable at x=1
  • · Replies 22 ·
Replies
22
Views
3K
Find eqn of Tangent Line to graph- Implicit Differentiation
  • · Replies 5 ·
Replies
5
Views
2K