The 2017 profits, $p$, in thousands of dollars, for Functions of America is modeled by $p\left(x\right) = −x^{4} + 21x^{3} − 138x^{2} + 280x$, where $x$ is months since January 1^st, 2017.

1. Approximate Functions of America’s profits for the first four months of 2017.

   Hint (a):

   Approximate the area under the curve over the interval $0\le x\le4$.

2. Approximate Functions of America’s profits for the first seven months of 2017.

   Hint (b):

   Approximate the area under the curve over the interval $0\le x\le7$.

3. What happened in May, June, and July?

   Hint (c):

   This can be answered using your results from parts (a) and (b).

4. Did Functions of America gain or lose money in 2017? How much?

   Hint (d):

   Approximate the area under the curve over the interval $0\le x\le12$.
   To get an accurate approximation, you will need to use a significant number of rectangle.