Assignment:
Q1. Determine the interval(s) where the function is increasing and the interval(s) where it is decreasing.
f(x) = 3x2 + x + 2
Q2. Determine the interval(s) where the function is increasing and the interval(s) where it is decreasing.
g(x) = x4 - 2x2 + 4
Q3. Find the relative maxima and relative minima, if any, of the following function. Show your work and the procedure.
f(x) = 3x4 -2x3 + 4
Q4. Suppose the total cost function for manufacturing a certain product is C(x) = 0.2(0.01x2 + 120) dollars, where x represents the number of units produced. Find the level of production that will minimize the average cost
Q5. The weekly demand for the Pulsar 25 color console television is p = 600 - 0.05x ( 0≤x≤12000)
where p denotes the wholesale unit price in dollars and x denotes the quantity demanded. The weekly cost function is given by
C(x) = 0.000002x3 - 0.03x2 + 400x +80000
where C(x) denotes the total cost incurred in producing x sets.
a) Find the revenue function R and the profit function P.
b) Find the marginal cost function C' , the marginal revenue function R' , and the marginal profit function P' .
c) Compute P'(2000) R’ and C’ (2000)Interpret each of these values.
Provide complete and step by step solution for the question and show calculations and use formulas.