Question

suppose the limit of f(x)=f(4) as x approaches 4 then..
a) f is differentiable at x=4
b) f is continuous at x=4
c) f is continuous and differentiable at x=4
d) f is differentiable but not necessarily continuous at x=4

Answer 1

c) f is continuous and differentiable at x=4

Answer 2

a function is continuous at a point \(x=a\) iff\[\lim_{x\to a}f(x)=f(a)\]a function is differentiable at \(x=a\) iff\[\lim_{b\to a}\frac{f(a)-f(b)}{a-b}=f'(a)\]

Answer 3

you are not given any information about the second criteria, hence...?

Answer 4

it is continuous?

Answer 5

yes