# Thread: Tangent line, math wrong somewhere

1. ## Tangent line, math wrong somewhere

I have an equation $f(x) = \frac{5x}{(3-5x)^5}$ 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 $f(2) = \frac{5(2)}{(3-5(2))^5} = -0.000595$

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

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

I get the equation of the tangent line should be $y = 0.00183x + 0.0043$ ,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.

2. ## Re: Tangent line, math wrong somewhere

Your y-intercept is wrong. Using your decimal approximations, you should have:

b = (-2)0.00183 + 0.000595 = -0.003065

3. ## Re: Tangent line, math wrong somewhere

Of course, there's no reason why you should be using decimal approximations anyway...

4. ## Re: Tangent line, math wrong somewhere

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

5. ## Re: Tangent line, math wrong somewhere

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

6. ## Re: Tangent line, math wrong somewhere

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.