Problem 1
Given y = f(x) = x^{2} + 2x +3
a) Use definitional formula given below to find out the derivative of the function.
b) Find out the value of the derivative at x = 3.
Problem 2
Given, y = f(x) = 2x^{3 }- 3x^{2} + 4x +5
a) Use Power function to find derivative of the function.
b) Find out the value of derivative at x = 4.
Problem 3
The revenue and cost functions for selling and producing quantity x for a certain production facility are given below.
R(x) = 16x – x^{2}
C(x) = 20 + 4x
a) Determine profit function P(x).
b) Use Excel to graph the functions R(x), C(x) and P(x) for interval 0≤ x ≤ 12. Copy as well as paste the graph below. Note: Use Scatter plot with smooth markers and lines.
c) find out the break-even quantities.
d) Determine average cost at the break-even quantities.
e) Determine marginal revenue R’(x).
f) Determine marginal cost C’(x)
g) At what quantity is the profit maximized?