The graph of y = f '(x), the derivative of f(x), is shown below. Given f(-4) = 2, evaluate f(4).
The options are:
0
2
8
10

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

answer: the correct answer is -32

step-by-step explanation:

ca = ec

cpctc makes it so that corresponding parts of the triangle you proved to be equal are equal, the other options aren't part of the part of the triangles you proved to be equal.