unit 1
What kind of function is g(x) = (1.2)^x
exponential
What is the instantaneous rate of change for a function, f(x) = .09x^3+4x^2-3x+90, at x=2
14.08
2^x
ln(2) (2^x)
what is the linearization function of a certain function with f(3) = 2 and f'(3)=-4?
2-4(x-3)
When ABC has been opened for 3 days, revenue is increasing by 10 hundred dollars per day
what is the limit at x = 1 and x = 4
1: 4
4: infinity
If a graph has a relative minimum at x=7, a zero at x=2, and an inflection point at x=6, at what x is the zero on the slope graph?
7
What does it mean for the function if the slope graph is below the x axis?
the function is decreasing
what are the two criteria for a critical point?
f'(c) = 0
f'(c) DNE
.06x^3-8.15x^2+150x+314.2 gives the production cost with x being the number of hours of production.
If f(6) = 933.76. what is the cost of producing the 7th hour?
992.44
write a sentence of interpretation for the following scenario: f(x) gives the number of people in a stadium, x minutes after the gates open. f'(28) = 12
28 minutes after the gates open, the number of people in the stadium is increasing by 12 people per minute.
Calculate the average rate of change, where x is years after 2000. AirTran posted a profit of 17.6 million at the end of 2009 compared with a profit of 12.6 million in 2007.
e^3x
3e^3x
What is the relative max of f(x) = 2x^3-5x+2 on the interval of [-2,2]. Is this the absolute max?
relative -.913
abs: 2,8
.06x^3-8.15x^2+150x+314.2 gives the production cost with x being the number of hours of production.
If f(6) = 933.76. what is the linearization formula?
933.76 + 58.68(x-6)
write a function that has constant change of 9 dollars per hour. when f(0) = 3
9x+3
Find the percentage rate of change at x=5 when f'(5)=6.5 and f(5)=18.2
35.714%
Find the derivative of a function defined g(x) * t(x) given the following information
g(2) = 3 g’(2) = -8
t(2) = 6 t’(2) = -1
-51
how many critical points are on the following graph?
3
When 3 thousand purses are produced, the cost of production is increasing by 12 hundred dollars per thousand purses. What is the marginal cost?
f'(3) = 1.2
To set aside money for emergencies, you place $2000 in an emergency savings account earning 3.5% interest compounded semi-annually. After 2 years and 8 months, your car breaks down and you need to withdraw all of the money from this account. How much will the account be worth at this time?
$2181.23
Use the numeric method to find the instantaneous rate of change of sales in 2011. Round to two decimal places.
f(x) = 1.546x2-7.894x+87.532 million units gives the yearly online sales of furniture, x years after 2005, 2<x<10. (6 from the left, 6 from the right...)
10.66
find the derivative funtion of
ln(x^3+2x^2+9x-4)
3x^2+4x+9/x^3+2x^2+9x-4
Draw the slope graph of a function with a relative minimum at x = 2
crosses x axis at x = 2 from negative to positive.
write a sentence of interpretation for the marginal cost for producing the 21st unit when f'(20) = 2 and f'(21) = 6
The additional cost of producing the 21st unit is 2 dollars.