A cubic function $f(x)$ with leading coefficient 1 satisfies $$f(1) = f(2) = 0, \quad f'(0) = -7$$ Let Q be the point where the line segment OP intersects the curve $y = f(x)$ other than P, where O is the origin and $\mathrm{P}(3, f(3))$. Let $A$ be the area enclosed by the curve $y = f(x)$, the $y$-axis, and the line segment OQ, and let $B$ be the area enclosed by the curve $y = f(x)$ and the line segment PQ. What is the value of $B - A$? [4 points] (1) $\frac{37}{4}$ (2) $\frac{39}{4}$ (3) $\frac{41}{4}$ (4) $\frac{43}{4}$ (5) $\frac{45}{4}$
A cubic function $f(x)$ with leading coefficient 1 satisfies
$$f(1) = f(2) = 0, \quad f'(0) = -7$$
Let Q be the point where the line segment OP intersects the curve $y = f(x)$ other than P, where O is the origin and $\mathrm{P}(3, f(3))$.\\
Let $A$ be the area enclosed by the curve $y = f(x)$, the $y$-axis, and the line segment OQ, and let $B$ be the area enclosed by the curve $y = f(x)$ and the line segment PQ. What is the value of $B - A$? [4 points]\\
(1) $\frac{37}{4}$\\
(2) $\frac{39}{4}$\\
(3) $\frac{41}{4}$\\
(4) $\frac{43}{4}$\\
(5) $\frac{45}{4}$