Extrema to the EXTREME
What goes up?
Thinking Conceptually
Bonus
100

Find all relative extrema. (Hints as the Min)

F(x) = (x-5)2


Relative Minimum: (5,0)

100

Determine the open intervals on which the graph is concave upward or concave downward.

y = x2 - x - 2


What is (-∞,∞)

100

What do you use F double prime to find?

What is Concavity
100

This person is a cool mom.

Who is Mrs. Weeks

200

Find all relative extrema. (Hint its the max)

F(x) = 6x - x2


Relative Maximum: (3,9)

200

Determine the open intervals on which the graph is concave upward or concave down 

g(x) = 3x2 - x3

Concave upward (-∞,1); Concave downward: (1,∞)

200

What does putting F double prime equal to 0 find?

What are inflection points
200

This person came from NORRIS!

Who is Hayden Richards

300

Find all relative extrema (Both mins and maxes)

g(x) = x2(6-x)3

(Hint: Nearest Tenth)

Relative maximum: (2.4,268.7)

Relative minimum: (0,0)

300

Determine the open intervals on which the graph is concave upward or concave downward

f(x) = 24 / x2 + 12

Concave upward: (-∞, -2), (2,∞)

Concave downward: (-2,2)

300

If F double prime is greater than zero, the function is ______.

What is Concave up
300

What person is known for his wanting to TRY all problems?

Who is Sam Wallman

400

Find all relative extrema (Both Mins and Maxes)

f(x) = x3 - 3x2 + 3

Relative maximum: (0,3)

Relative minimum: (2,-1)

400

Determine the intervals where the function is concave up and/or concave down.

f(x) = 4x3 + 8x2

Concave up: (-2/3, ∞)

Concave down: (-∞,-2/3)

400

How do you find Concavity?

What is plugging in numbers around Inflection points into double prime (- or +).

400

What day did everyone celebrate in Differentiated Chemistry? (10/22)

What is Mole Day

500

Find all relative extrema (Mins and Maxes)

f(x) = x + 4/x

Relative maximum: (-2,-4) 

Relative minimum: (2,4)

500

Find whether  the intervals on which the Graph are a concave up and/or concave down

f(x) = x2 + 1/x2 - 1

Concave up: (-∞, -1), (1,∞)

Concave down: (-1,1)

500

How do you find relative extrema (mins/maxes) for Concaves? 

What is Use the second derivative test to plug in critical points into the second derivative to determine Mins/Maxes

500

What is the worst Apple (Mrs. Weeks' Favorite)?

What is Honeycrisp

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