- #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!
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!