State the conditions on f that are needed to guarantee that there is a number c in the interval a < x < b such that
f '(c) = (f(b) − f(a)) / (b − a)
Select all that apply.
A. f must be differentiable on a < x < b.
B. There are no conditions on f.
C. f must be continuous on a ≤ x ≤ b.
D. f must be differentiable on a ≤ x ≤ b.
E. f must be continuous on a < x < b.
I thought that it was C and D, which would then imply A and E as well, so I submitted A, C, D, E, but I got it wrong. Then I tried just A and E, but I got it wrong again. I only have one chance left though. I don't think it would be B, so I want to think the site is just stupid and wants me to only put C and D, but I wanted to make sure before submitting my last chance.
Could you please explain your answer?
Thank you!
f '(c) = (f(b) − f(a)) / (b − a)
Select all that apply.
A. f must be differentiable on a < x < b.
B. There are no conditions on f.
C. f must be continuous on a ≤ x ≤ b.
D. f must be differentiable on a ≤ x ≤ b.
E. f must be continuous on a < x < b.
I thought that it was C and D, which would then imply A and E as well, so I submitted A, C, D, E, but I got it wrong. Then I tried just A and E, but I got it wrong again. I only have one chance left though. I don't think it would be B, so I want to think the site is just stupid and wants me to only put C and D, but I wanted to make sure before submitting my last chance.
Could you please explain your answer?
Thank you!
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I think it's B.
Look at this picture: http://gyazo.com/ddc02df79c65aec6e253a9d…
The function is not continue and not differentiable, but it fulfills f '(c) = (f(b) − f(a)) / (b − a)
Look at this picture: http://gyazo.com/ddc02df79c65aec6e253a9d…
The function is not continue and not differentiable, but it fulfills f '(c) = (f(b) − f(a)) / (b − a)