Question

1. Determine the absolute minimum and maximum values of the function f(x) = x^3 - 6x^2 + 9x + 1 in the following intervals:

a) [0,5]

b) [-1,2]

2. A company produces and sells x number of calculators per week. The functions for demand and cost are the following:

p = 500 - 0.5x and c(x) = 10,000 + 135x.

Determine:

a) Function of weekly revenue

b) Price and number of calculators that have to be sold to maximize revenue

c) Function of weekly profit

d) Price and number of calculators that have to be sold to maximize profit

3. Use the criteria of the second derivative to determine the max and min relatives of the function f(x) = x^4 - 8x^2 + 16

Answer 1