d) Find the maximum for the function and the
A farmer wishes to enclose a rectangular region
bordering a river with fencing, as shown in the diagram.
Suppose that x represents the length of each of the three parallel
pieces of fencing. She has 600 feet of
Solve for y =_________________
a) If the length of each of the three parallel pieces is x, then the length of the remaining side in terms of x is:
b) The restriction on x is:
c) The function that represents the area of the
fenced region is: A= L times W = ______ times __________
d) Find the maximum area and the dimensions .
e) What would the dimensions be for an area of
22,500 square ft?
A piece of sheet metal is 2.5 times as long as it is wide. It is
to be made into a box with an open top by cutting 3-
inch squares from each corner and folding up the sides. Let x
represent the width of the original piece of sheet
a) The restriction on x is x > 6 why?
b) Determine a function that represents the volume:
c) For what value of x will the volume of the box be 600?
e) For what value of x will the volume of the box be 800?
d) For what values of x will the volume of the box be between 600 and
A kite is flying on 50 ft of string. How high
is it above the ground if its height is 10 feet more than the
horizontal distance from the person flying it? Assume the string is
being held at ground level.
When Respect Brings Success charges
$600 for a seminar on management techniques, it attracts 1000
For each decrease of $20 in the charge, an additional 100
people will attend the seminar. Let x represent the
number of $20 decreases in the charge.
a) Determine a revenue function R that will give revenue generated as a
function of x, the number of $20
Revenue= Price X Number Sold
b) Find the value of x that maximizes the revenue.
What should the company charge to maximize the revenue?
c) What is the maximum revenue the company can generate?
Local maxima--- the highest point at a peak.
Local Minima----the lowest point at a valley
Degree give the number of possible x-intercepts
Copy the graph from your calculator and locate and
label the local maxima and minima.
Absolute Maxima--- the highest
point at a peak is also the highest point on the graph.
Absolute Minima----the lowest point at a valley is also the lowest point
on the graph.
If there is an absolute maximum and/or minimum , then label them.
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