Answer
No such function exists.
(see "step by step" for proof)
Work Step by Step
SUPPOSE such a function exists.
Then, according to the Mean Value Theorem
there exists $c\in(-2,2)$ such that
$f^{\prime}(c)=\displaystyle \frac{f(2)-f(-2)}{2-(-2)}=\frac{6+2}{4}=2.$
But, the text states that $f^{\prime}(x)< \mathrm{l}$ for all $x.$
We hve a contradiction, meaning that what we SUPPOSED above is wrong.
No such function exists.
