Haskell

[J Brown]

hi, I am only a beginner of programming with Haskell,
how do I define each of the following:

* maxFirst :: (Int,Int) -> (Int,Int) -> (Int,Int) 

which returns, of its two input tuples, the one whose
first component is the highest.

* Define a function

maximumFirst :: [(Int,Int)] -> (Int,Int)

which returns, from its list of input tuples, the
tuple whose first component is highest, assuming input
list is non-empty.

A function is given:

maxf :: [Int] -> Int

such that if maxf [x1,....,xn] = xi then

elem xi [x1,...,xn] == True
f xi >= f x1
f xi >= f x2
......
fxi >= f xn

* How do you define the function maxf (above) which
returns the element of its non-empty input list for
which f is maximal.
*and to define a function minf which returns the
element from its non-empty input list for which f is
minimal.

*how do I define the function

maxIndexf :: [Int] -> Int

such that if 

maxf xs = i

for non-empty xs, then

0 <= i < length xs
f (x s !! i) >= f (x s !! 0)
f (x s !! i) >= f (x s !! 1)
....
f (x s !! i) >= f (last xs)

that is it returns the index of the element of its
input list for which f is maximal.

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