5. Pictured is the graph of $f(x) = \frac{x^3}{4} - \frac{x^2}{2} - \frac{x}{2} + 3\cos(x)$ and a line, $l$, which is tangent to $f(x)$ at the point $(0, 3)$.
a. Find the area of Region R. You may use technology to find the root of $f(x)$.
b. Find the equation of line $l$ if it is tangent to the graph of $f(x)$ at $(0, 3)$.
c. At what ordered pair, other than $(0, 3)$, does the graph of line $l$ intersect the graph of $f(x)$? You may use technology to find this point, but show how you got there.
d. Find the area of Region S. You may use technology to find the intersection point(s).
