Find k such that the line is tangent to the graph

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Discussion Overview

The discussion revolves around finding the value of k such that the line represented by the equation 4x - 9 is tangent to the graph of the function x^2 - kx. The scope includes mathematical reasoning and problem-solving related to tangents and intersections of curves.

Discussion Character

  • Mathematical reasoning, Homework-related, Exploratory

Main Points Raised

  • One participant expresses uncertainty about the problem and seeks guidance on how to approach it.
  • Another participant suggests that the solution involves finding a point of intersection and ensuring the slopes of the function and line are equal at that point.
  • A different viewpoint proposes a non-calculus approach, indicating that for the line to be tangent to the function, the equation 4x - 9 = x^2 - kx must have only one solution, which relates to the discriminant of the quadratic equation.
  • There is a light-hearted exchange regarding a deleted post, indicating a mistake was made, but the nature of the mistake is not specified.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as multiple approaches to the problem are discussed, and uncertainty remains regarding the best method to find k.

Contextual Notes

There are limitations regarding the assumptions made about the discriminant and the conditions under which the line is tangent to the curve, which remain unresolved.

kdinser
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I'm not sure what they are looking for here.

Find k such that the line is tangent to the graph of the funtion

Function: x^2-kx Line: 4x-9

Just need a little push in the right direction.
 
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Hints:
You must find 2 features:
a) A point in common between the graphs of your function and your line.
b) That the slope of the function at that point equals the line's slope

This is a system of two equations!
Solutions to this system is what you are looking after (a k-value will be one of the numbers in a given solution, a x-value of the point of intersection will be the other number)
 
thanks, I'll give it a shot.
 
A solution that doesn't involve calculus: if the line is supposed to tangent the other function, then the equation 4x - 9 = x^2 - kx may only have one solution. If you solve this for x, what can you say about the discriminant?
 
arildno, did you see your mistake (in the deleted post), or did you remove it in order to not rouse my anger? :wink:
 
That's why I deleted my dumb message..
 

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