The graph below shows a company's profit f(x), in dollars, depending on the price of pencils x, in dollars, being sold by the company:
part a: what do the x-intercepts and maximum value of the graph represent? what are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (6 points)
part b: what is an approximate average rate of change of the graph from x = 2 to x = 5, and what does this rate represent? (4 points)

Afactory makes propeller drive shafts for ships. a quality assurance engineer at the factory needs to estimate the true mean length of the shafts. she randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. the lengths are known to follow a normal distribution whose standard deviation is 2 mm. calculate a 95% confidence interval for the true mean length of the shafts. input your answers for the margin of error, lower bound, and upper bound.