# Tangent Line

• Nov 11th 2012, 11:03 PM
camjenson
Tangent Line
thanks
• Nov 11th 2012, 11:12 PM
MarkFL
Re: Tangent Line
The line tangent to a function $\displaystyle f(x)$ at $\displaystyle x=c$ (assuming the derivative exists at this point) is found by the point slope formula:

$\displaystyle y-f(c)=f'(c)(x-c)$

Writing this in slope-intercept form, we have:

$\displaystyle y=f'(c)x+(f(c)-cf'(c))$

Now, using $\displaystyle f(x)=\frac{1}{\ln(bx)}$ and $\displaystyle c=\frac{e}{b}$ can you now compute the required $\displaystyle y$-intercept?
• Nov 11th 2012, 11:19 PM
camjenson
Re: Tangent Line
To be honest, no, I don't know where those variables would go in the equation...
• Nov 11th 2012, 11:25 PM
MarkFL
Re: Tangent Line
First, compute the derivative of $\displaystyle f(x)=\frac{1}{\ln(bx)}$. Next, let $\displaystyle x=c=\frac{e}{b}$ and evaluate the yintercept:

$\displaystyle f(c)-cf'(c)$
• Nov 11th 2012, 11:30 PM
camjenson
Re: Tangent Line
Isn't this the derivative -1/(x*[(ln(x))^(2)])?
So, in more simpler words, isn't it y-y1=m(x-x1)? y being the intercept y1 being the derivative after putting e/b in for x, m being the derivative, x being 0, and x1 being e/b?
• Nov 11th 2012, 11:39 PM
MarkFL
Re: Tangent Line
Your derivative is correct, and next you correctly cite the point-slope formula for a line, but after that you contradict yourself/make wrong statements, and I am not sure what you really mean. I think what I stated is about as simple as it gets.