Name
MATH 115 MIDTERM III Please work out each of the given problems.
Credit will be based on the steps that you show towards the final answer.
Show your work. PROBLEM
1 Without the use of your graphing
calculator, A)
Determine the relative extrema if
any. B)
Determine where the function is
increasing and decreasing. C)
Determine the inflection points if
any. D)
Determine where the function is
concave up and concave down. E) Use parts A through D to sketch the graph of the function. I. y = x^{3} - 12x II. y = 3x^{4} - 4x^{3} III.
3x - 4 IV.
x PROBLEM
2
You manage the new Spockwood ski resort. Your research shows that if you charge $40
per lift ticket, you can expect to sell 3000
tickets. For every
$5 increase in price you can expect to lose 250 customers.
Assume the demand equation is linear. A)
Find the demand equation. B)
What price will yield the maximum revenue? C)
Is the demand elastic or inelastic when the price is $45? PROBLEM
3 At the blood bank, a
cylindrical bottle without top is to contain 100 cc
of blood. What should the
dimensions of the bottle be in order to minimize material costs?
Assume that the glass has the same thickness throughout. PROBLEM 4 The department of fish and game have introduced a species of trout that was once native to the region. The number (in hundreds) of this species t years after their introduction can be modeled by the equation
90(2 + 5t) |