Derivative of a Line - A Newbie Question

In summary, The conversation is about a theorem on a line's derivative in the context of "Elementary Calculus: An Approach Using Infinitesimals". The person is confused about the theorem and gives an example to illustrate their confusion. They then realize their mistake and thank the other person for their support. They also mention their nationality but acknowledge that it is off-topic.
  • #1
danne89
180
0
Hi again! Time for one more of my newbie questions.
I'm reading "Elementary Calculus: An Approach Using Infinitesimals
" http://www.math.wisc.edu/~keisler/calc.html and can't get a theorem on a lines derivative. It goes like this:
[tex]f(x)=kx+b \Rightarrow \frac{dy}{dx} = f'(x) = k[/tex]

That doesn't make seens to me because the definition of a tangent line is
g(x)=f'(x)(x-a)+b, there (a, b) is the point of the tangent.

For instance, let's say f(x)=2x. The f'(x)=2, using the above theorem. And then the tangent for the point (2, 2) ought to be l(x)=2(x-2)+2=2x-4+2=2x-2. But it's parallell to f(x)=2x! What am I doing wrong, please give me a hint!
 
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  • #2
Eeh, the point is (1,2), not (2,2), so:
l(x)=2(x-1)+2=2x
 
  • #3
Ohh. I took a point OUTSIDE the line. I feel so dumb...
 
  • #4
Thanks for the support. By the way, many from Scandinavia here, isn't. The reson to care is that I'm a Swede. Anyway, maybe enought OT talk now.
 

FAQ: Derivative of a Line - A Newbie Question

What is a derivative of a line?

A derivative of a line is a measure of how much the line is changing at a particular point. It represents the slope of the line at that point.

How is the derivative of a line calculated?

The derivative of a line is calculated using a mathematical formula, called the derivative formula, which involves finding the slope of a line between two points on the line and then taking the limit as those two points get closer together.

Why is the derivative of a line important?

The derivative of a line is important because it allows us to understand the rate at which a quantity is changing. It is also used in many real-world applications, such as physics, economics, and engineering.

How is the derivative of a line related to the concept of tangent?

The derivative of a line is related to the concept of tangent because it represents the slope of the line at a particular point, which is the same as the slope of the tangent line at that point. The tangent line is a line that touches the curve at only one point and is used to approximate the behavior of the curve near that point.

Can the derivative of a line be negative?

Yes, the derivative of a line can be negative. This means that the line is decreasing or sloping downwards at that particular point. A positive derivative indicates that the line is increasing or sloping upwards at that point. A derivative of zero indicates a horizontal line.

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