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1.

(2 + a) ^{2} f″(1) (2 – a)^{2} f″(– 1) = 0

(2 – a) ^{2} f″(1) – (2 + a)^{2} f″(– 1) = 0

f′(1) f′(–1) = (2 – a)^{2}

f′(1) f′(–1) = – (2 + a)^{2}

2.

f(x) is decreasing on (–1, 1) and has a local minimum at x = 1

f(x) is increasing on (–1, 1) and has a local maximum at x = 1

f(x) is increasing on (–1, 1) but has neither a local maximum nor a local minimum at x = 1

f(x) is decreasing on (–1, 1) but has neither a local maximum nor a local minimum at x = 1

3.

g′(x) is positive on (–∞, 0) and negative on (0, ∞)

g′(x) is negative on (–∞, 0) and positive on (0, ∞)

g′(x) changes sign on both (–∞, 0) and (0, ∞)

g′ (x) does not change sign on (–∞, ∞)