Homework Problem Intermediate Value Theorem

[headintheclouds17]

(Equitable Cake Cutting). a) Suppose that F and G are two continuous functions on an
interval a  x  b, and that F(a)  G(a) but F(b)  G(b). Show that the equation F(x) = G(x)
is satisfied for some x on the interval. (Hint: apply the intermediate value theorem to a suitable
combination of F and G.) b) By applying a), show it is possible to cut any circular cake through
its exact center so that the two halves have exactly the same amount (area) of icing, no matter
how unevenly the cake may have been iced.

 

[mmm4444bot]

What is the meaning of the Intermediate Value Theorem, to you ?

 

[headintheclouds17]

Isnt it that there exists a value of c in the interval of [a,b]?

 

[mmm4444bot]

Isnt it that there exists a value of c in the interval of [a,b] ?

The answer to this question is yes because that is not a correct interpretation of the Intermediate Value Theorem.

I mean, on the Real number line, we can always find an infinite number of values between any two points a and b, so it's trivial to say only "there exists a value of c in the interval of [a,b]".

I'm thinking that you should learn what the Intermediate Value Theorem says, before attempting the posted exercise.