Answer:
2
Step-by-step explanation:
f'(x) is an odd function (symmetrical about the origin), therefore f(x) is an even function (symmetrical about the y-axis). So f(x) = f(-x).
Since f(-4) = 2, f(4) = 2.
We can also show this using integrals:
f(-4) = ∫₀⁻⁴ f'(x) dx + C
2 = ½ (-4)(-2) + C
2 = 4 + C
C = -2
f(4) = ∫₀⁻⁴ f'(x) dx − 2
f(4) = ½ (4)(2) − 2
f(4) = 4 − 2
f(4) = 2
