Assignment:
Q1. The cost and the revenue functions (in dollars) for a frozen yogurt shop are given by:
C(x)= 400x +400/ x +4 and
R(x)=100x
Where x is measured in hundreds of units
A=Graph C(x) and R(x) on the same set of axes
B=What is the break-even point for this shop
C=If the profit function is given by P(x), does P(1) represent a profit or a loss ?
D= Does P(4) represent a profit or a loss?
Q2. The average cost (in dollars) per item of manufacturing x thousand cans of spray paint is given by:
A(x) = - .000006x^4 +.0017x^3 + .03 x^2- 24x + 1110
How many cans should be manufactured if the average cost is to be as low as possible? What is the average cost in that case?
Q3. Use the definition of the derivative to find the derivative of the function
Y=x^3 +5
Q4. Find the slope of the Tangent line to the given curve at the given value of x. Find the equation of each tangent line
Y=8-x^2; at x=1
Q5. Find the derivative of each of the given function
g(t)=t^3 + t-2 /(2t - 1)^5
The total energy Consumption in Quadrillion BTU for the US can be approximately by the function
f(x)=-0.00144x^3+ 0.014151x^2 +0.1388x + 23.35
Where x=0 corresponds to the year 1970
- Find the energy consumption for 1990, 2000 and 2008
- Find the average rate of change in energy consumption between 2000 and 2008
- At what rate was energy Consumption changing in 2008
Q6. The Net Revenue for Chase Bank can be approximated by the function
g(x)= - .033741x^4 +1.62176x^3 - 28.4297x^2 +216.603x- 599.806 (9 <_( less than or = to) x less than or equal to 18)
- Find the revenue in 2006
- Find the revenue in 2008
- Find the rate of change of revenue in 2007
Q7. Find the absolute extrema of each function on the given interval
f(x)=x^4 -18x^2 +1;[-4,4]
Q8. A restaurant has an annual demand for $900 bottles of a California wine. It costs $1 to store one bottle for 1 year and it costs $5 to place a reorder. Find the number orders that should be placed annually.
Provide complete and step by step solution for the question and show calculations and use formulas.