For the function $f$ given above, determine whether the following conditions are true. Input T if the condition is true, otherwise input F .

(a) $f'(-1)=0;$
(b) $f'(1)$ does not exist;
(c) $f'(x)<0$ if $|x|<1$;
(d) $f'(x)>0$ if $|x|>1$;
(e) $f''(x)<0$ if $x\not=1$. .