1. ## Implicit Differentiation Help

I am dumbfounded on what I am doing wrong with this problem. I was given the following problems.

Find the equation of the tangent line to the curve (a hyperbola)
at the point . The equation of this tangent line can be written in the form where
m=
b=

2. Bump!

3. Originally Posted by jwebb19
I am dumbfounded on what I am doing wrong with this problem. I was given the following problems.

Find the equation of the tangent line to the curve (a hyperbola)

at the point . The equation of this tangent line can be written in the form where
m=
b=

the slope is equal to:

$
m=\frac{dy}{dx}
$

Now we differentiate the equation for the curve with respect to $x$:

$
\frac{d}{dx} \left[ \frac{x^2}{16} - \frac{y^2}{4} \right]=0
$

$
\frac{2 x}{16} - \frac{2 y}{4} \frac{dy}{dx} =0
$

so:

$
\frac{dy}{dx}=\frac{x}{4y}
$

Now plug in the values of $x$ and $y$ to find $dy/dx$ which gives you your $m$.

Finaly plug the values of $m,\ x,$ and $y$ into the equation for the line abd find $b$

RonL