Derivatives
What is the derivative of x3 - x2 + x?
3x2 - 2x + 1
Find the integral of 4x4 - 3x3 - 2x2 - x + 1
(4/5)x5 - (3/4)x4 - (2/3)x3 - (1/2)x2 + x + C
A hole is a type of _________ discontinuity.
Removable
What does the slope on a distance-time graph represent?
Velocity
What is Mr. Stofer's first name?
Kevin
What is the derivative of 3(x2 - x)2 ? Do not simplify.
6(x2 - x)(2x - 1)
Find the integral of 2x2 on the closed interval from 2 to 10.
661.33
What are the 2 conditions that must be met for Mean Value Theorem to apply?
1. must be on closed interval [a,b]
2. must be differentiable on (a,b)
Draw the graph of the derivative of y = 2x + 3.
Notecard 1
Who are the two publishers of our textbook?
Larson, Edwards
What is the derivative of 2xe3x ? Simplify.
2e3x(3x+1)
Find area between the graphs of y = x2 and y = x from the vertical lines x =1 to x = 3.
1/6
How do you find the average value of a function?
Multiply the integral of a function (from a to b) by 1/(b-a)
If g(x) is the inverse of f(x), what will be true of their slopes at any given x value? Give an example.
The slope of g(x) will be inverse of the slope of f(x).
Example: If the slope of f(1) is 2, the slope of g(1) is 1/2.
Name 3 industries that use calculus.
Physics, engineering, economics, medicine, statistics...
What is the derivative of lnx / 2x ?
(2 - 2lnx) / (4x2)
Find the volume of a solid rotated around the x-axis bound by the graphs of y = x2 and y = x on the interval from 0 to 1. Leave in terms of pi.
2(pi)/15
What theorem is this an example of?
Integral of f(x) from a to b equals F(b) - F(a).
Fundamental Theorem of Calculus
Draw a slope field for the differential equation dy/dx = x2y (on a square grid from -1 to 1 on both axes).
Notecard 2
Who is primarily accredited with the invention of calculus?
Isaac Newton
What is the derivative of arctan x ?
1 / (1 + x2)
What is the volume of a solid rotated around the y-axis bound by the graphs of y = 1 and y = x. Leave in terms of pi.
(pi)/3
Write the derivative of a function in the form of a limit.
lim(as h approaches 0) of [f(x+h) - f(x)]/h
Draw the graph of the integral of sinx (from 0 to two pi).
Notecard 3
When were the first AP tests given (year)?
1956