Find k such that the line is tangent to the graph

In summary, The conversation is discussing how to find a value for k that will make the line tangent to the graph of the function x^2-kx. The person is given hints on how to solve the problem, including finding a point of intersection and setting the slopes of the function and line equal to each other. The conversation also mentions that there is a solution that does not involve calculus and that the equation 4x - 9 = x^2 - kx may only have one solution if the line is tangent to the function. It is suggested that the person should check the discriminant to determine the number of solutions. One of the speakers also acknowledges a mistake they made in a previous post.
  • #1
kdinser
337
2
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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  • #2
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)
 
  • #3
thanks, I'll give it a shot.
 
  • #4
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?
 
  • #5
arildno, did you see your mistake (in the deleted post), or did you remove it in order to not rouse my anger? :wink:
 
  • #6
That's why I deleted my dumb message..
 

1. What is the definition of a tangent line?

A tangent line is a line that touches a curve at only one point, without crossing it. It is perpendicular to the radius of the curve at that point, and it represents the instantaneous rate of change at that point.

2. How do you find the slope of a tangent line?

The slope of a tangent line can be found using the derivative of the function at the point of tangency. This can be done by taking the limit of the difference quotient as the change in x approaches 0, or by using the power rule for derivatives.

3. Can there be more than one tangent line to a curve at a given point?

No, there can only be one tangent line at a specific point on a curve. This is because the tangent line represents the instantaneous rate of change at that point, and there can only be one instantaneous rate of change for any given function at a specific point.

4. What is the significance of finding the tangent line to a curve?

Finding the tangent line to a curve is important because it allows us to understand the behavior of the curve at a specific point. It can also be used to approximate the value of the function at that point, and to find the slope of the curve at that point.

5. Are there any real-world applications of finding the tangent line to a curve?

Yes, there are many real-world applications of finding the tangent line to a curve. For example, it can be used in physics to analyze motion and acceleration, in economics to determine marginal cost and revenue, and in engineering to optimize designs and models.

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