# Thread: Find the equation of the tangent line?

1. ## Find the equation of the tangent line?

Find the equation of the tangent line to the graph of the function at z=3

2. Find the derivative of the function using the quotient rule:

$\displaystyle f(x) = \dfrac{6z^2}{5z^2 + 2z}$

$\displaystyle f'(z) = \dfrac{(5z^2 + 2z)(12z) - (6z^2)(10z + 2)}{(5z^2 + 2z)^2}$

Put z = 3.

$\displaystyle f'(3) = \dfrac{(5(3)^2 + 2(3))(12(3)) - (6(3)^2)(10(3) + 2)}{(5(3)^2 + 2(3))^2}$

Simplify, then find the value of f(z) when z = 3.

Then use:

$\displaystyle y = mx+ c$

m is f'(3), and c is a constant.

To find c, use y = f(3) and x = z

You'll get your equation of the line now. You can replace y and x by f(z) and z respectively.

3. WOW. I did that and it kept turning out wrong. Turns out I used an x instead of z.
I'm really smart.
Thank you =)

4. You're welcome