Using f'(x)
Using f''(x)
Absolute Extrema
100

Find the critical points of the function y=x3-9x2-21x-11

x = -1 and x = 7

100

Using the second derivative test, find any local minimums of the function f(x) = 2x3 - 6x + 2

local min @ x = 1

local max @ x = -1

100
Determine the absolute min and max for the following equation on its given interval f(x) = 5x^2 + 3x -5, -2 ≤ x ≤ 0
Min is (-0.3, -5.45) Max is (-2 ,9)
200

For the function y=3x2-2, is x = 0 a local min or local max? Show how you know using the first derivative test. 

local min (derivative switches from negative to positive)

200

Find any inflection points of the function f(x) = x3 - 9x2 -21x - 11

x = 3

200
Determine the absolute min and max for the following equation on its given interval f(x) = (1/6)*x^2 + x^(1/3), 0 ≤ x ≤ 2
min is at (0,0) max is at (2, 1.93)
300

Find the all local extrema of the function f(x) = x3 - 3x - 6 using the first derivative test. Be sure to specify which points are local minimums and which are local maximums. 

x= -1 is a local maximum

x=1 is a local minimum

300

Which of the following is NOT an inflection point for the function f(x) = 3x5 - 5x4  and why?

x= 0 or x = 1



x = 0 is not an inflection point (second derivative doesn't change sign)

300
Determine the absolute min and max for the following equation on its given interval f(x) = x^4 - (2x+1)^2, -2 ≤ x ≤ 0
min is (0, -1) max is (-2, 7)
400

The following is the derivative of a function. Use it to find all local minimums and maximums of the function (state which are minimums and which are maximums). 

f'(x)=6(x+1)(x-2)2

x= -1 is a local minimum, there are no local maximums


400

Given the derivative of a function f'(x) = 6(x+1)(x-2) find any points of inflection of the function. 

x = 1/2

400
A farmer has a 1000m of fencing and he wishes to enclose an area on his farm with three equal partitions. What dimensions will maximize the area of the enclosure? What area would that result in?
The dimensions are 125m by 250 m The resulting area is 31,250 m^2
500

The following is the derivative of a function. Find the interval(s) on which the function is increasing. 

f'(x) = 2(x-3)(x+1)(x-4)

-1 < x < 3 U x > 4

500

On what interval(s) is the function f(x) = 0.25x4 +2x3 +4.5x2  concave down?

-3 < x < -1

500

Find the length of the shortest ladder that will reach over an 8-ft. high fence to a large wall which is 3 ft. behind the fence https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/maxmindirectory/MaxMin.html

17.64 ft Solution https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/maxminsol3directory/MaxMinSol3.html#SOLUTION 18

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