If cost in dollars is C(x)=100,000 + 160x, what is the fixed cost?
$100,000
100
C(x)=100+24x-x^2. What is the average cost function?
(100/x)+24-x
100
If f''(a)<0, the curve at x=a is concave ____. If x=a is a critical point, the graph has a relative ___ at x=a.
down; maximum
100
Your cost to produce y sandwiches and x salads is given by C(x,y)=4+2x+3.5y. If you make 3 sandwiches and 4 salads, what is your total cost?
$24
200
Calculate d/dx[x^2 - x^4]
2x - 4x^3
200
You have found that elasticity for a laptop at price p is given by E=p/(10,000 - p). At a price of $2000, is the laptop inelastic, elastic, or unit elastic? Should the manufacturer increase or decrease price to increase revenue?
E=0.25; inelastic; raise price to increase revenue
200
Find all critical points of g(x)=1/x.
None. g'(x) is undefined at x=0, but so is g(x). [see "warning" on page 2 of lecture notes 5.1 part 1]
200
Your rent is $700 a month, you spend $100 each time you go grocery shopping, and your electricity costs $11 per hour used. Find an expression B(s,t) for your monthly bills when you shop s times per month and use t hours of electricity.
B(s,t) = 700 + 100s + 11t
300
Name a synonym for "derivative."
Slope of tangent line, instantaneous rate of change, limit of the average rate of change as h goes to 0, limit of the difference quotient at the point as h goes to 0. (note: just "average rate of change" is NOT an acceptable answer - that's a different thing)
300
In 1893, there were approximately 1600 AIDS cases in the US. By 1895, there were 8100 cases. Find an exponential model A(t) for the number of AIDS cases, with t=0 corresponding to the year 1980. Round to 2 decimal places if necessary.
A(t)=140.47 * 2.25^t
300
Use the first derivative test to find the coordinates of the relative extrema of f(x)=x^3 - 27x on the domain [-5,5].
Relative maxima (-3,54) & (5,-10). Relative minima (3,-54) & (-5,10)
300
f(x,y)=3x-5y. For every 1 unit increase in x, f (increases/decreases) by ___ units
increases by 3 units
400
The price of gold is given by G(t) = 5t^2 - 85t +1,762, where t is the number of hours since 7:30 (7.5). Find the average rate of change of the price of gold between 8:00 and 9:30.
(.5,1720.75) (2,1612) -> avgROC= -72.5
400
Differentiate f(x)=2*3^(2x+1) + 10e^(3x+1)
f'(x)=4ln(3)*3^(2x+1) + 30e^(3x+1)
400
Find relative extrema using the second derivative test. h(x)= x^3 - 3x^2 - 9x. (Only need to find x values and whether min or max)
min at x=3;max at x=-1
400
Calculate dk/dx and dk/dy for k(x,y)=x/y
dk/dx=1/y ; dk/dy=-x/(y^2)
500
Find an equation for the tangent line to the graph of f(x)=2x^2 - 5x + 5 at x=5. Use the form y=mx+b.
y=15x-45
500
Profit when selling q laptops is given by P= -200,000 + 4,000q - 0.4q^2 - 0.00001q^3. The number of laptops made is determined by the number n of workers employed and is given by q=100n. At what rate is profit changing with respect to the number of workers when the company employs 20 workers? Include units.
228,000 dollars per worker.
500
You are fencing in a rectangular area along a river (so you need to fence 3 sides). Fencing costs $8 a foot. You want to fence in 180 sq ft. What dimensions will minimize cost? Keep exact numbers and round to 2 decimals at the end.