Which of the following statements is/are true? (5 points)
I. If f '(x) 0 on (a, b), then f(x) is increasing on [a, b].
II. If f(a) = f(b), then there exists a number c in (a, b) such that f '(x) = 0.
III. If f(x) is differentiable at x = c, then f(x) is continuous at x = c.

Question

Which of the following statements is/are true? (5 points)
I. If f '(x) > 0 on (a, b), then f(x) is increasing on [a, b].
II. If f(a) = f(b), then there exists a number c in (a, b) such that f '(x) = 0.
III. If f(x) is differentiable at x = c, then f(x) is continuous at x = c.

rhondasommer · Answer

what do you think?

chris215 · Answer

i think its one and three

rhondasommer · Answer

i think you are correct but let me doube check. @Mr_Perfection_xD

chris215 · Answer

oh ok thank you !!

rhondasommer · Answer

@tkhunny was she correct?

tkhunny · Answer

I is good.
II is the intermediate value theorem.
III Does differentiability require continuity?

chris215 · Answer

III Does differentiability require continuity?
 no it doesnt

tkhunny · Answer

It was a little bit of a trick question.  The standard proof is that Differentiability IMPLIES continuity.

Now what do we think?

chris215 · Answer

ohh ok thats true then

rhondasommer · Answer

thanks @tkhunny i was a little confused :)

tkhunny · Answer

Do we get to mark all three true?

chris215 · Answer

no :/