Solve the below:
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.
f(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 where p denotes the wholesale unit price in dollars and x denotes the quantity demanded. The weekly cost function is given by
p=600-0.05x(0<=x<=12000)
where denotes the total cost incurred in producing x sets.
C(x)=0.000002x^3-0.03x^2+400x+80000
a) Find the revenue function R and the profit function P.
b) Find the marginal cost function , the marginal revenue function , and the marginal profit function .
c) Compute R' and C' (2000)Interpret each of these values.