I know how to get this derivative thing, but I don't understand what is meant by the slope at a given point.
For exemple, for $f(x)=-2/x$ the derivative is $f'(x)=2/x^2$
Now how do I get this slope thing at $c=-1$?
$\endgroup$ 71 Answer
$\begingroup$The derivative gives you the slope at a point. For a given curve, if a tangent line exists, there is one unique derivative value, which is the slope at a point. If it helps, recall that the definition of derivative is $$ f'(x)=\lim_{h\rightarrow0}\frac{f(x+h)-f(x)}{h} $$ Now what that intuitively is without the limit is the slope of the line between points $x$ and $x+h$. If we let $h\rightarrow0$, that is just the slope at the point $x$. There is more to it, and it can be hard to believe at first, but just trust us for now :)
So in your case, $f(x)=\frac{-2}{x}$ so you correctly calculated $f'(x)=\frac{2}{x^2}$. This gives you the slope at any point $x$ where $f'(x)$ is defined. Now go ahead and plug $x=-1$ in to get $$ f'(-1)=\frac{2}{(-1)^2}=2 $$
This video might also help you out
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