Parallel Tangents to Cubic Graph

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SUMMARY

The discussion centers on finding a tangent line parallel to the tangent of the cubic function f(x)=(x+1)(x+4)(x+6) at x=-6, which has a slope of 10. The user, flyinghigh, successfully identified the slope but seeks a method to algebraically determine another tangent line with the same slope. The solution involves setting the derivative of the function equal to 10 to find the corresponding x-values where the tangent lines are parallel.

PREREQUISITES
  • Understanding of cubic functions and their properties
  • Knowledge of derivatives and how to compute them
  • Familiarity with tangent lines and their equations
  • Basic algebraic manipulation skills
NEXT STEPS
  • Learn how to compute derivatives of polynomial functions
  • Study the concept of tangent lines and their slopes
  • Explore methods for solving equations involving derivatives
  • Practice finding parallel tangents for various polynomial functions
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Students studying calculus, particularly those focusing on derivatives and tangent lines, as well as educators seeking to enhance their teaching methods in algebra and calculus.

flyinghigh
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Homework Statement


I have the graph of a function f(x)=(x+1)(x+4)(x+6). I've found the tangent at x=-6, the equation of which is y=10x+60. I then need to algebraically find the equation of another tangent on the curve which is parallel to the first.

Homework Equations


No idea.

The Attempt at a Solution


Since I'm graphing this on Autograph I've managed to find a point where the tangent is parallel to the first, but since this can be done without the computer program I'm really interested to know how it's done. So yeah, I know that the tangent I'm trying to find will have a gradient of 10 but that's about it...

Any help would be great,
flyinghigh
 
Physics news on Phys.org
Okay, you know you're looking for a tangent line with a slope of 10.

Can you write an equation for the slope of the tangent (as a function of x), and set that equal to 10?
 

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