TITLE: Finding x when slope = 1
QUESTION [1 upvotes]: I've been working out some problems relating to slope on the points of a curve. I'm having issues with this one: In the curve to which the equation is... $$x^2 + y^2 = 4$$
find the value of $x$ at those points where the slope $= 1$. I thought to differentiate and then set $\frac{dy}{dx}$ equal to $1$ and solve for $x$. This seems right but even differentiating this particular equation was confusing to me. As always, many thanks in advance for any help on this.

REPLY [2 votes]: A simple Hint:
When $F(x,y)=0$ defines $y$ as a function of $x$ implicitly, as above, then we have $$y'=\frac{-F_x}{F_y}$$ in which $F_x$ means the partial differential of $F$ with respect to $x$. 

Note that if you want to use this way, you should make sure that the relation $F(x,y)=0$ make a functional relation between $y$ and $x$.
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