Question

the function f(x) is continuous on the closed interval [a,b]. which must be true?
a) f(x) has a max on [a,b]
b) f(x) has a point of inflection [a,b]
c) f ' (c)= f(b)-f(a)/b-a for at least one c in the interval [a,b]
d) f ' (c) = 0 for at leastone c in the interval [a,b]
e) f(x) has a critical value on the interval [a,b]

Answer 1

I am thinking a.

Answer 2

dont think so - there could be a minimum

Answer 3

extreme value theorem

Answer 4

the extreme value theorem states that if a real-valued function f is continuous in the closed and bounded interval [a,b], then f must attain a maximum and a minimum, each at least once.

Answer 5

A could be true, but depends on what you mean by max.

Answer 6

I would go with the extreme value theorem....

Answer 7

there is more than one correct answer

Answer 8

also the function could be a straight line

Answer 9

well a is definitely one of them

Answer 10

the max of y=3 on [a,b] is 3

Answer 11

b,c,d are all out. we need differentiable for c, and continuity does not imply differentiable (the opposite is true). for b, f(x) = 3 has no inflection point on [a,b], and for c y=x has no zero derivative. So the only other option is e, and im not sure if that is true.

Answer 12

oh it doesn't say it's differentiable, sorry. I thought it did.

Answer 13

and e is out.

Answer 14

yeah you're right

Answer 15

ok so the answer is a, thanks guys helped me out a lot

Answer 16

yes a is correct

Answer 17

for the record, c would be right as well if it were differentiable

Answer 18

correct, very sneaky.

the way I remember differentiable implies continuity and not the other way around is
DC comics. D first then C. And the fact that |x| is not differentiable on R.