The graph of y = f ′(x), the derivative of f(x), is shown below. given f(4) = 6, evaluate f(0). a. -2 b. 2 c. 4 d. 10

B. 2

Explanation:

From the graph we get

(1). for  

(2). for  

(3). for

Now let us take the anti derivative of the second function, and we get

for

We find from the condition :

Thus we have

.

Now we find the anti derivative of the first function, and get

What we note now is that the function is continuous because the derivative of the functions is defined at and at .

since the function are continuous,

Thus we have

Now we can easily evaluate

Which is choice B.