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zeesbrat3
 one year ago
Which one of the following statements is true?
zeesbrat3
 one year ago
Which one of the following statements is true?

This Question is Closed

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0Which one of the following statements is true? A.) If f is continuous on a closed interval [a, b], then f attains an absolute maximum value and f attains an absolute minimum inside the interval [a, b]. B.) If f ′′(c) = 0, then x = c is an inflection point on the graph of f(x). C.) If f ′′(x) < 0 on the interval (a, b), then f is concave up on the interval (a, b). D.) None are true.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1well second derivative test does determine concavity

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0I remember there used to be a rule involving c, but I haven't studied this in 6 month so I am rusty. Can you explain?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1haven't studied this in years, but still remember parts of it

Tommynaut
 one year ago
Best ResponseYou've already chosen the best response.1Tricky question. A) Can you think of any sort of curve or line that wouldn't have a maximum and minimum value in a domain? What is the definition of an absolute maximum/minimum? Does a horizontal line have an absolute maximum and minimum? B) What is always true when the second derivative at a point is 0? C) What is the difference between f''(x) > 0 and f''(x) < 0? Which one means concave up, which one means concave down?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1we need the theorems/definitions

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0f''(x) < 0 i concave down

Tommynaut
 one year ago
Best ResponseYou've already chosen the best response.1Yep. It's a good question for you to look through your textbook or research online for, if you're unsure on definitions. This question is just testing your memory. And yes, 2nd deriv < 0 means down, > 0 means up. So C can't be true.

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0is* sorry. My keyboard i being temperamental

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1for all x in some interval f''(x) <0 is concave down and f''(x) >0 is concave up.

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0And on a closed interval, you don't necessarily have both a max and a min

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1this question is just matching theorems and definitions about graphing inflection, concavity, and continuity.. a calculus I topic. So at least we don't have to do that much. It's hard to type and eat pizza at the same time xD

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0Hahaha I feel your pain

Tommynaut
 one year ago
Best ResponseYou've already chosen the best response.1Can you give me an example where you wouldn't have a maximum and a minimum?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1what about a graph that only has the absolute maximum?

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0Wait, does absolute max and min necessarily mean a real max/min? I'm not sure if I made sense..

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1hmm absolute max  highest point in the graph absolute min  lowest point in the graph relative max  a high point in the graph relative min  a low point in the graph

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1dw:1436409136021:dw

Tommynaut
 one year ago
Best ResponseYou've already chosen the best response.1We're talking about a closed domain. In a closed domain, there would always be a highest and lowest value. The reason the question is tricky is because of option B. A lot of people think that f''(x) = 0 is enough to say a point is a point of inflection, but this isn't necessarily true.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1if it's equal, f''(x) = 0 then it's neither a max or a min. It's just a constant

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1point of inflection is that particular area where the line changes from negative to positive. or vice versa

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0Oh! I mistook absolute min for a real min. Can yall help me with one more of this type?

Tommynaut
 one year ago
Best ResponseYou've already chosen the best response.1I mean, like in the example, if x=c and f''(c) = 0, this isn't enough information to say that there's a point of inflection at x=c.

Tommynaut
 one year ago
Best ResponseYou've already chosen the best response.1And a point of inflection is where the concavity of the line changes.

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0Thank you. Ya, I read up on the point of inflections, but never really grasped it. It's weird..

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0Which one of the following statements is true? A.) If f ′′(x) > 0 on the interval (a, b) then f(x) is concave down on the interval (a, b). B.) If f ′(x) > 0 on the interval (a, b) then f(x) is increasing on the interval (a, b). C.) If f ′(c) = 0, then x = c is a relative maximum on the graph of f(x). D.) None of these are true.

Tommynaut
 one year ago
Best ResponseYou've already chosen the best response.1An example where f''(c) = 0 is not an inflection point is for the function y = x^4. It's like a fat parabola, so it obviously has no point of inflection (it's always concave up). However, f''(0) = 0, but x=0 is actually a minimum.

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0So A is wrong, because it is the opposite of what it should be

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0If there is a hip, there is a point?

Tommynaut
 one year ago
Best ResponseYou've already chosen the best response.1I'm not sure what you mean by that. But yes, you're right about A being wrong. B looks like it's right, so now look at C... does that look wrong to you? If f'(c) = 0, then sure, at x=c we MIGHT have a relative maximum, but it might be a minimum, or a saddle point.

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0I'm sorry, a saddle point? @Tommynaut

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0By hip, I meant a cubed function

Tommynaut
 one year ago
Best ResponseYou've already chosen the best response.1You might know a saddle point as a horizontal point of inflection (so f'(x) = 0 and f''(x) = 0).

Tommynaut
 one year ago
Best ResponseYou've already chosen the best response.1I'm off now, hope I helped

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1I've heard of saddle, but it was for my Mathematical Biology class last semester. If a 2 x 2 matrix has one negative eigenvalue and one positive eigenvalue, then it's a saddle and that's always unstable. The graph looks like this dw:1436410099737:dw

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1\[\det(A \lambda I) = 0 \] is what I used

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0Honestly, I have never seen those symbols before in my life

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1http://www.math.psu.edu/tseng/class/Math251/Phase_portrait_reference_card.pdf

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1I think that saddle graph is a variation.. my book had what I drew
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