Math 121 Test 3 University of Alabama Boxmeyer Questions fully solved & verified for accuracy(A+graded)

relative max and min of 49x + 36/x type problems shortcut

Square root of 36/49. Plug back into f(x)

If you get 0 as a critical number, but f(0)=0

F(0) will not be a max or min

If you only get one critical number it will always be a

Minimum and not a maximum*

*at least for this test

T/t-4 with the closed interval [5,9] shortcut

Max: (x,x)

Min: (y,y/x)

Example- (5,5) , (9,9/5)

Concave upward/downward shortcut polynomial

Upward: (-infinity, sq rt of # by x^2)

Downward: (sq rt of # by x^2, infinity)

Concave upward/downward shortcut fraction

Upward: (-infinity, sq rt),(sq rt, infinity)

Downward: (-sq rt, sq rt)

"Discuss concavity of the graph of...."

Half, half, full, full

Greater than, less than, greater than

Upward, downward, upward

Relative extrema or x + 16/x shortcut

Max: (-sq rt, -half)

Min: (sq rt, half)

For curvy graph remember

-,+,-

For U shaped graph remember

Positive U

For perimeter

Divide by 4

For area

Take sq rt

"The owner wants the field to contain 180,000 square meters..." shortcut

Y=180,000 x 2, sq rt of 360,000, 600/2

X=180,000 x 2, sq rt of 360,000

Point of diminishing returns on graph is point where

Graph is rising and the graph actually hit a direct point in correlation to the y-axis

To find "number of units x that produces max revenue..." R=135x^2-0.06x^3

Get derivative of R, isolate x, then divide

To get "Minimum average cost per unit c bar..."

Get c bar, isolate x, solve

G(x)=e^x^7-8x, (-1,e^7) shortcut

Y=-e^7x

X^y-ey-2=0 will always equal

2xy/e^y - x^2

E^xy + x^2 - y^2 will always equal

ye^xy + 2x/2y - xe^xy

P=72e^-0.000025x

A. 72e^-0.000025(40,000)

B. (72)(40,000)(e^-0.000025(40,000))

Y=ln(x)/x^3 type shortcut

1-exponent ln(x)/x^+1

Example: 1-3 ln(x)/x^4

Ln 8+e^x/8-e^x type shortcut

1st number x 2 + e^x/1st number^2 - e^2x

Example: 16+e^x/64-e^2x

Y=ln(x^5/2) type shortcut

Exponentx - exponent

Example: 5/2x - 5/2

Ln xy + 4x = x type shortcut

-y/x - number

Example: -y/x - 4y