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Review
Local Max/Min
Snack Drawer
Stationary Pts. of Inflection
Non-stationary Pts. of Inflection
100
Liz isn't sure where that 2 came from, so she creates an equation to help her find the answer: 0 = x^2 - 4 +4 Find x.
X = 2
100
There is a stationary point at (0, -5) on the graph of y=x^2 -5. Is it a local maximum or minimum?
Local minimum.
100
Two fathers and two sons sat down to eat eggs for breakfast. They ate exactly three eggs, each person had an egg. Derive the reason this is possible. (Hint: this doesn't actually involve deriving.)
One of the 'fathers' is also a grandfather. Therefore the other father is both a son and a father to the grandson. In other words, the one father is both a son and a father.
100
What are the 3 types stationary points?
Local maximums & minimums, and points of inflection
100
FREE AUTOMATIC 100 POINTS!
Good job.
200
Find the derivative of the function y = 5x^7 + 2x^5 + x^6 + 2x
y' = 35x^6 + 10x^4 + 6x^5 + 2
200
One day, Liz drinks all of Caroline's water. (More like everyday but anyway). She's a nice person so she goes to fill it up, and when she comes back, she tosses it to Caroline. The water bottle's journey through space is given by the function y=x^2 - 8x - 10. Find the stationary point that marks the local maximum.
(2, -22). Local minimum.
200
What do you get if you divide the circumference of a pumpkin by its diameter?
Pumpkin pi.
200
Find the stationary point of inflection for the function y = x^4 - 3x^3 +2.
Stationary point of inflection: (0,2).
200
Define "non-stationary point of inflection".
A point of inflection whose second (instead of first) derivative equals zero.
300
On what day do we take our IB Calculus Paper 1?
May the Fourth be with you on this one.
300
One day, Liz is driving her car innocently to school when an alien ship abducts her, including the car. Liz is not about to explain to her parents why her car got lost in space, so she yells FACTORIALS! at the aliens until they get scared and drop her car. The arc formed by her brief journey towards the sky is given by the function y= -x^2 + 3!x. Find the local maximum.
Local maximum: (3, 16)
300
In which of the two snack drawers are the Cheez-Its currently?
The second.
300
Make at least 5 words out of the word INFLECTION.
Example of acceptable answers: ICE, ONCE, FINE, NET, COT.
300
What time did Caroline and Emma get done with the project last night?
Midnight. :)
400
What do you call the fourth derivative of a function?
Jounce
400
Find one local maximum and one local minimum for the function y=3x(cosx). Range: [0, 5] Hint: You may use your calculator after you derive, in order to find the x values. Give the two final coordinates using three significant figures.
Local maximum: (0.860, 1.68) Local minimum: (3.43, -9.87)
400
What is brown and sticky?
A stick.
400
What's the non-mathematical definition for "inflection"?
1. a change in the form of a word (typically the ending) to express a grammatical function. synonyms: stress, accent 2. the modulation of intonation or pitch in the voice.
400
This is a really easy question. The team who picked the question wins 400 points, even if they get the question wrong. .......Who is currently yelling about how unfair this question is?
Probably Juan or Amalia, depending what team they're on.
500
If you can do this within 60 seconds of opening this question, you get an extra 100 points! If you can't, the other team gets that 100 points and you finish solving the problem. Derive: y=5(x^1/2) (3!x)
y' = (5/2x^1/2)(6x^2) + 60x(x^1/2)
500
Amalia is repeatedly annoyed by a certain Calc student, so she finally ends up throwing him across the room. As he flies towards the back wall, his position in space, 's' meters above the ground, after time 't' seconds, is given by the handy dandy function, s= -7(x - 3)^2 + 3x +4. At what time does Juan reach the peak of his short-lived flight? (Give answer rounded to three sig figs.)
3.21 seconds
500
A farmer is trying to cross a river. He is taking with him a rabbit, carrots and a fox, and he has a small raft. He can only bring 1 item a time across the river because his raft can only fit either the rabbit, the carrots or the fox. How does he cross the river. (You can assume that the fox does not eat the rabbit if the man is present, you can also assume that the fox and the rabbit are not trying to escape and run away)
Take the rabbit. Go back and get the fox, take it across, and switch it with the rabbit. Take the rabbit back, and switch it with the carrots. Take the carrots, then go back for the rabbit.
500
One day Mrs. Bergman walks into her room, ready for a great day of teaching trig identities, when Evelyn, peer-pressured by Juan, jumps out of her hiding place and yells WHAT'S UP MRS. BERGMAN! Mrs. Bergman is so surprised that she yells back, INTEGRALS!, an substitute expletive that Ted would approve of. The inflection of her voice is so extreme that her Calc students use it's function, y = (2x-3)^3 (x+2), to find the inflection point, because we're curious like that. What are the coordinates of the point they found?
Stationary point of inflection: (3/2, 0)
500
Find the non-stationary point of inflection for the function y=2x^4 - 3x^3 +2x. Three sig figs.
Non-stationary point of inflection: (0.750, 0.867)