Thread: prove or desprove claims

determine if the following are correct or wrong
if correct prove if not then show counter example:
a)if and for then

couldnt find counter example ,i thought f(x)=x but there is not g(x)
to desprove it

b) for x>0
i was told told to use the theore, of lagrange
in which the derivative in some point is the slope between two points
but i dont know how to use it

c)f(x) if bound from the top on (0,1{]}
if f(x) is continues from the left of x=1 then sup f((0,1))>=f(1)

d)if f(x) is integrabile on {[}a,b{]} and if
then there is

so

Originally Posted by transgalactic

[LEFT]
determine if the following are correct or wrong
if correct prove if not then show counter example:
a)if and for then

couldnt find counter example ,i thought f(x)=x but there is not g(x)
to desprove it

(a) how about and for a counter-example?

determine if the following are correct or wrong
if correct prove if not then show counter example:
a)if and for then

couldnt find counter example ,i thought f(x)=x but there is not g(x)
to desprove it
b) for x>0
i was told told to use the theore, of lagrange
in which the derivative in some point is the slope between two points
but i dont know how to use it
c)f(x) if bound from the top on (0,1{]}
if f(x) is continues from the left of x=1 then sup f((0,1))>=f(1)
d)if f(x) is integrabile on {[}a,b{]} and if
then there is

so

(a)
I like your idea. How about ?

(d)
is the following function continuous?

if so you can use the intermediate value theorum, as its trivial to show that there are values of g(c) on either side of 1.

yes thanks
1 down 3 to go

regarding b) i was told to turn into

so i need to prove that f(x)>0 for x>0
f(0)=0
now i need to show that f'>0 so f will be monotonicly increasing

how to conclude that f' is positive for x>0