Define
F(x)=7(x2−1)(x2+2x+3).
(a) Find F′(x) and write your result as a single simplified polynomial.
(b) Factorise F′(x) completely.
(c) Evaluate F′(1) and F′(−1), and comment on any symmetry you observe.
(d) Using your factorised form, determine all real intervals on which F(x) is increasing.