zeesbrat3
  • zeesbrat3
Which one of the following statements is true?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
zeesbrat3
  • zeesbrat3
Which 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.
zeesbrat3
  • zeesbrat3
Please help
UsukiDoll
  • UsukiDoll
well second derivative test does determine concavity

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

zeesbrat3
  • zeesbrat3
I 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
  • UsukiDoll
haven't studied this in years, but still remember parts of it
Tommynaut
  • Tommynaut
Tricky 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
  • UsukiDoll
we need the theorems/definitions
zeesbrat3
  • zeesbrat3
f''(x) < 0 i concave down
Tommynaut
  • Tommynaut
Yep. 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
  • zeesbrat3
is* sorry. My keyboard i being temperamental
UsukiDoll
  • UsukiDoll
for all x in some interval f''(x) <0 is concave down and f''(x) >0 is concave up.
zeesbrat3
  • zeesbrat3
And on a closed interval, you don't necessarily have both a max and a min
UsukiDoll
  • UsukiDoll
this 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
  • zeesbrat3
Hahaha I feel your pain
Tommynaut
  • Tommynaut
Can you give me an example where you wouldn't have a maximum and a minimum?
UsukiDoll
  • UsukiDoll
what about a graph that only has the absolute maximum?
zeesbrat3
  • zeesbrat3
Wait, does absolute max and min necessarily mean a real max/min? I'm not sure if I made sense..
UsukiDoll
  • UsukiDoll
hmm 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
  • UsukiDoll
|dw:1436409136021:dw|
zeesbrat3
  • zeesbrat3
Ohh
Tommynaut
  • Tommynaut
We'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
  • UsukiDoll
if it's equal, f''(x) = 0 then it's neither a max or a min. It's just a constant
UsukiDoll
  • UsukiDoll
point of inflection is that particular area where the line changes from negative to positive. or vice versa
zeesbrat3
  • zeesbrat3
Oh! I mistook absolute min for a real min. Can yall help me with one more of this type?
Tommynaut
  • Tommynaut
I 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
  • Tommynaut
And a point of inflection is where the concavity of the line changes.
UsukiDoll
  • UsukiDoll
^ yeah...
zeesbrat3
  • zeesbrat3
Thank you. Ya, I read up on the point of inflections, but never really grasped it. It's weird..
zeesbrat3
  • zeesbrat3
Which 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
  • Tommynaut
An 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
  • zeesbrat3
So A is wrong, because it is the opposite of what it should be
zeesbrat3
  • zeesbrat3
If there is a hip, there is a point?
Tommynaut
  • Tommynaut
I'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
  • zeesbrat3
I'm sorry, a saddle point? @Tommynaut
zeesbrat3
  • zeesbrat3
By hip, I meant a cubed function
Tommynaut
  • Tommynaut
You might know a saddle point as a horizontal point of inflection (so f'(x) = 0 and f''(x) = 0).
zeesbrat3
  • zeesbrat3
Oh okay
Tommynaut
  • Tommynaut
I'm off now, hope I helped
zeesbrat3
  • zeesbrat3
You did, thank you
UsukiDoll
  • UsukiDoll
I'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
  • UsukiDoll
\[\det(A- \lambda I) = 0 \] is what I used
zeesbrat3
  • zeesbrat3
Honestly, I have never seen those symbols before in my life
UsukiDoll
  • UsukiDoll
http://www.math.psu.edu/tseng/class/Math251/Phase_portrait_reference_card.pdf
UsukiDoll
  • UsukiDoll
I think that saddle graph is a variation.. my book had what I drew
UsukiDoll
  • UsukiDoll
http://tutorial.math.lamar.edu/Classes/DE/PhasePlane.aspx

Looking for something else?

Not the answer you are looking for? Search for more explanations.