Question

If f is differentiable at x=c, which must be true?
1) f is continuous at x=c
2) f' is continuous at x=c
3) f' is continuous at y=c
4) f is continuous at y=c

Answer 1

f is continuous at x=c

Answer 2

and that is given by 3 conditions,
one,
f(x) exists

two,\[\lim_{x \rightarrow c}f(x)~~~\tt exi sts\]

three,
\[\lim_{x \rightarrow c}f(x)=f(c)\]

Answer 3

once you prove the third condition though, then the 1st 2 are obviously present.