Suppose that the following information is known about a function $f$: the graph of its derivative, $y = f'(x)$, is given in the figure below. Further, assume that $f'$ is piecewise linear (as pictured) and that for $x \le 0$ and $x \ge 6$, $f'(x) = 0$. Finally, it is given that $f(0) = 1$.

On what interval(s) is $f$ an increasing function? (Separate multiple intervals with a comma.)
Answer:

On what intervals is $f$ a decreasing function? (Separate multiple intervals with a comma.)
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On what interval(s) is $f$ concave up? (Separate multiple intervals with a comma.)
Answer:

On what interval(s) is $f$ concave down? (Separate multiple intervals with a comma.)
Answer:

At what $x$ value(s) does $f$ have a relative minimum? (Separate multiple points with a comma.)
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At what $x$ value(s) does $f$ have a relative maximum? (Separate multiple points with a comma.)
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Recall that the Total Change Theorem tells us that $$f(1) - f(0) = \int_0^1 f'(x) \, dx.$$ What is the exact value of $f(1)$?
$f(1)=$

Use the given information and similar reasoning to the previous question to determine the exact value of the following:
$f(2)=$ ,
$f(3)=$ ,
$f(4)=$ ,
$f(5)=$ ,
$f(6)=$ .

Based on your responses to all of the preceding questions, which of the following is an accurate graph of $y=f(x)$? ? A B C D