Identify whether these statements are SOMETIMES TRUE, ALWAYS TRUE or NEVER TRUE, show your Complete Explanations (This is all about Calculus: Continuity and Differentiability of a Function) . a. If a...

Identify whether these statements are SOMETIMES TRUE, ALWAYS TRUE or NEVER TRUE, show your Complete Explanations
(This is all about Calculus: Continuity and Differentiability of a Function).

a.
If a function is differentiable at a point, then it is continuous at the same point.
(Explain WHY)

b.
If a function is continuous at a point, then it is differentiable at the same point.
(Explain WHY)

c.
If a function is differentiable at a point, then it is not continuous at the same point
(Explain WHY)

d.
If a function is not differentiable at a point , then it is continuous at the same point.
(Explain WHY)

e.
If function is not differentiable at a point, then it is not continuous at the same point.
(Explain WHY)

I already provided the answers I just need the COMPLETE EXPLANATIONS.




a. ALWAYS TRUE




b. SOMETIMES TRUE




c. NEVER TRUE




d. SOMETIMES TRUE




e. SOMETIMES TRUE