By the fundamental theorem of calculus, we have that a continuous function always has a primitive. However, if I take f(x) = absolute value of x, that f function is continuous, but does not have a primitive. That sounds a contradiction to the FTC. What am I missing here?
Thank you!
The function $$F(x)=\frac{1}{2}x\left|x\right|$$ has derivative $|x|$. Not sure why you'd say $|x|$ does not have a primitive.
$|x|$ does not have a derivative at $x=0$, but a primitive is an anti-derivative, not a derivative.