help i was betrayed by mathematics ♡

the derivative function has betrayed us

worked example: What is the equation of the tangent line to the graph of $f (x) = x^{5} + 3 x^{2} + 2 x$ at the point where $x = - 1$ ?

We need to find $f^{'} (x)$ first

$f^{'} (x) = 5 x^{4} + 6 x + 2$

Now we find $f^{'} (- 1)$

$f^{'} (- 1) = - 9$

Now we know the slope is -9

but you know, we now graph $f (x)$ and the slope should be 1, not -9

what?

the explanation on khan academy is, is… what?