Note that f satisfies the conditions for the mean value theorem to be

applicable on [2,11].

Suppose f(11)<22, then by the mean value theorem there exists a c in (2,11)

such that:

f'(c)=(f(11)-f(2))/9 = (f(11)-4)/9,

but if f(11)<22 this is <2, which contradicts the assumption that f'(x)>=2.

Now let f(x)=4+2(x-2), then f'(x)=2 for x in (2,11), and f(11)=22.

Therefore f(11) can be as small as 22 and no smaller.

RonL