Question

How do you use implicit differentiation to find the slope of the curve given `x^2+y^2=25` at (3,-4)?

Answer 1

I found: `3/4`

Explanation:

We first differentiate (implicitly) remembering that `y` itself will represent a function of `x` so in differentiating it we need to include this information writing a `(dy)/(dx)` term.
So we have:
`2x+2y(dy)/(dx)=0`
rearrange:
`(dy)/(dx)=-x/y`

This expression will represent the inclination/slope `m` of your function.

Considering your point we substitute `x=3 and y=-4` to find the specific slope at that point:
`m=(dy)/(dx)=-3/(-4)=3/4`