Decide whether each of the following statements is true or false. If true, explain why. If false, give a counter-example and explain why the counter-example contradicts the statement.
Suppose F(x) is differentiable at ALL x in R.
Suppose lim x->0 f '(x) = L, does it follow that f '(0) = L?
Differentiability and limits are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.