Unit 5
What do we call the values of x for which f'(x)=0?
Critical points
integrate 6x^2
2x^3 + C
how do you find the area between two curves?
integrate (upper function - lower function)
solve for y
dy/dx = 6 + cos(x)
y = 6x + sin(x) + C
When is your Final?
May 20th
When f'(x)=0 and f"(x)=0, x is a?
Inflection point
2/3x^(3/2) + C
Describe the DISC method and how to set it up.
pi times the integral of radius squared; where the radius is the function being used.
solve for y
y'=8x/y
y=sqrt(8x^2+C)
When is the last day of classes for Seniors?
May 23rd
When f'(x)=0 and f"(x)>0, x is a?
Minimum
integrate x+2 between -1 and 4
17.5
Describe the WASHER method and how to set it up.
pi times the integral of the bigger radius square minus the smaller radius squared; where the radii are different functions from the problem.
sketch a slope field given dy/dx=2x
should look like x^2
How many years has Alec been at SPCPA?
3
Find any/all mins, maxes, and inflection points for
1/3x^3 - 1/2x^2 - 6x + 1
Min at x=3
Max at x=-2
I.P. at x=1/2
Name one of the the two ways an integral can be considered "improper"
Infinity in the bounds
OR
Discontinuous over the bounds
find the volume of the solid generated by the region bounded by y=x^2, y=0, x=4 rotated around the x-axis.
1024pi/5
sketch a slope field given dy/dx=cos(x)
should look like sin(x)
When is our last day of school?
May 29th
You have 600 feet of fencing for a garden. You want to form a rectangle and use some of the fence to split it half down the middle. What dimensions for the length and width will maximize your growing area?
100 ft by 150 ft
Integrate with u-sub: 3x^2(x^3+4)^5
1/6(x^3+4)^6 + C
Find the volume created bit square cross sections perpendicular to the x-axis over the region y=2x+1 between x=0 and x=3
57
find y given the equation below and the specific point (0, 1).
dy/dx=6x/5y
y=sqrt(6/5x^2+1)
What club has Alec been hosting afterschool this year?
Fiber Arts!