# Tangent line, math wrong somewhere

• Oct 22nd 2012, 08:24 PM
AZach
Tangent line, math wrong somewhere
I have an equation $\displaystyle f(x) = \frac{5x}{(3-5x)^5}$ and I want the equation of the tangent line at x = 2. I know what to do, but my math is wrong somewhere down the line.

Subbing in 2 $\displaystyle f(2) = \frac{5(2)}{(3-5(2))^5} = -0.000595$

Taking derivative $\displaystyle f'(x) = \frac {100x+15}{(3-5x)^6}$ and then plugging in 2 $\displaystyle f'(2) = \frac {100(2)+15}{(3-5(2))^6} = 0.00183$

So, I use equation of a line now that I have the solutions for f(x) and m.... $\displaystyle -0.000595 = 0.00183(2) + b$ and I wind up with $\displaystyle b = 0.0043$

I get the equation of the tangent line should be $\displaystyle y = 0.00183x + 0.0043$ ,but this is incorrect, and I was hoping somebody could eyeball this if they get a chance because I think I'm going in circles trying to fix it.
• Oct 22nd 2012, 08:40 PM
MarkFL
Re: Tangent line, math wrong somewhere

b = (-2)0.00183 + 0.000595 = -0.003065
• Oct 22nd 2012, 08:42 PM
Prove It
Re: Tangent line, math wrong somewhere
Of course, there's no reason why you should be using decimal approximations anyway...
• Oct 22nd 2012, 08:45 PM
AZach
Re: Tangent line, math wrong somewhere
I see how your math works, but why did you change 2 to a -2?
• Oct 22nd 2012, 08:51 PM
AZach
Re: Tangent line, math wrong somewhere
Quote:

Originally Posted by Prove It
Of course, there's no reason why you should be using decimal approximations anyway...

True.
• Oct 22nd 2012, 08:53 PM
MarkFL
Re: Tangent line, math wrong somewhere
Quote:

Originally Posted by AZach
I see how your math works, but why did you change 2 to a -2?

Think of the point-slope formula for a line.

Also, I agree with the above, I would use the true rational values...because we can. :)