Derivatives
Find the derivative of y = 3x^2 sin x
3x^2 cos x + 6x sin x
The derivative of a function is a ________ finder.
What is slope
Find the critical points of f(x)=2x^3-6x^2+2.
Build a rectangular pen with three parallel partitions using 500 feet of fencing. What dimensions will maximize the total area of the pen? (give the area, and the dimensions)
What is x=50 ft. and y=125 ft. and A = 6250 ft.2 is the largest possible area of the pen.
In what year was OMG started to
1917
f(x) = (3x - 2x^2)(5 + 4x)
-24x^2 + 4x + 15
The slope of the tangent line is the ___________ rate of change.
What is instantaneous
Use the First Derivative Test to find the relative min and relative max for f(x)=x^3-27x-20.
What is relative max at (-3,34) and relative min at (3,-74).
Construct a window in the shape of a semi-circle over a rectangle. If the distance around the outside of the window is 12 feet, what dimensions will result in the rectangle having largest possible area ?
What is x=approx 2.33 ft. and y=3 ft. ,then A =approx 6.99ft.^2 is the largest possible area of the rectangle.
What do the 100 folds in a chefs hat represent?
The 100 ways to cook an egg
Find the derivative of y = (5x - 2)/(x^2 + 1)
(-5x^2 + 4x + 5)/(x^2 + 1)^2
The slope of the line tangent to f(x) = 4x^(3/2) at x = 9
What is 36
Use the first derivative test to find the relative max and min of f(x)=3x^4+8x^3-6x^2-24x.
What is relative mins at (-2,8) and (1,-19) and relative max at (-1,13).
How many equations is typically needed in order to create an optimization problem?
2
What is the name of a mammal that lays eggs?
Monotremes
Find the derivative of f(x) = (2x + 5)/(x)^1/2
(2x - 5)/(2x^(3/2))
The slope of the line tangent to f(x) = sin (x) at x=0
What is 1
The 2nd derivative shows?
Concavity
What do you call a group of bunnies?
A Fluffle
f(x) = sin3 4x Find f'(x)
12sin^2 4x cos 4x
The equation of the line tangent to f(x) = 8x - 2x^2 at (3,6).
What is y = -4x + 18
Use the second derivative test to find the critical points, inflection points, concavity, and the graph of the function: f(x)=x^4-4x^3+10.
What is critical points: (0,10) and (3,-17), inflection points: (0,10) and (2,-6), concave up at x=3.
What is the speed of a computer mouse measured in?
Mickey's