Week 1-2
Week 3-4
Week 5-6
Week 7-8
100
What is a practical versus a mathematical domain?
Practical: What makes sense in the context of the problem, ex. percentage is 0-100
Mathematical: All possible values that fit within the function's domain
100
Determine whether or not the function is continuous for all real numbers
F(x)={x+3, if x<1
F(x)={x^3-x+4, if x>=1
F(1)=(1)^3-(1)+4=4
Lim x->1^-)=(1)+3=4
Lim x->1^+)=(1)^3-(1)+4=4
F(x) is continuous for all real numbers
100
Find the derivative of g(t)=(4t2-3t+2)-2 and write the answer as a fraction.
(-2(8t-3))/((4t2-3t+2)-3)
100
The function f(a) represents the taxable income (in thousands of dollars) for an
individual with federal tax rate a (as a percentage). The equation f(5) = 20 means...
An individual with a taxable income of 20 thousand dollars has a federal tax rate of 5%
200
If
f(x)=x^3*g(x), g(-7)=2, g'(-7)=-9,
determine the value of
f'(-7)
3381
200
What is the derivative of the following function at x = 2?
f'(2) = 1
200
If the second derivative is POSITIVE, the linear approximation is... (overestimate/underestimate) - Draw a graph to show your thinking
Underestimate
200
Where do you find critical values?
Where do you find inflection points?
Where f' = 0 or f' = undefined
Where f''=0 or f''= undefined
300
Daily demand for a commodity is inversely proportional to its price, with 1200
cubic meters demanded daily when priced at 3.90 Euro per cubic meter. Supply of
the commodity is proportional to its price, with 5000 cubic meters supplied when
price is 2 Euro per cubic meter.
At what unit price does market equilibrium occur?
sqrt(4680/2500)
D(p)=4680/p
S(p)=2500p
4680=2500p^2
300
Compute the following and put your answer in one fraction:
d/dx(x/(x-3))
-3/(x-3)^2
300
If the second derivative is NEGATIVE, the linear approximation is... (overestimate/underestimate) - Draw a graph to show your thinking
Overestimate
300
Find the critical value(s) of f(x) = x2-4x-12
f'(x) = 2x - 4
0 = 2x - 4
4 = 2x
x = 2
400
a. 1
b. -1
c. infinity
400
Identify the break-even point, given a demand of q = 72 − 3p items produced when charging p dollars per item, and total cost C = 5q dollars.
Which answer makes sense given the context?
The break-even point occurs when 45 items are produced and sold at $9 each.
400
What is marginal analysis? What does it show us?
A way of approximating the change associated with increasing production by ONE unit.
C(x+1) - C(x) = Cost to produce one more item
R(x+1) - R(x) = Revenue from selling one more item
P(x+1) - P(x) = Profit from selling one more item
400
Find the critical values of g(n) = n3-3n2-9n
Then determine the intervals of increasing and decreasing
n = 3 and n = -1
Increasing: (-inf, -1) U (3, inf)
Decreasing: (-1,3)
500
lim x-> ∞
(x^5+3x+4)/(1-x^4)
-∞
500
d/dx[(2x^2-8x)/(5x^2)]
500
What is the estimated total profit in selling 101 items if P(100) = 10,150 and P'(100) = 89?
Total profit in producing 100 items = 10,150
Approx cost to produce the 101st item = 89
Total cost to produce 101 items = 10,239
500
If they exist, find the critical values, intervals of increasing/decreasing, inflection values, and interval of concavity for the following function
f(x) = x^2-4x
Critical Value: x=2
Inc: (2,inf) Dec: (-inf, 2)
No inflection values. F''(x) is always positive so f(x) is always concave up (-inf,inf)