Question

Which one of the following statements is true?

Answer 1

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.

Answer 2

Please help

Answer 3

well second derivative test does determine concavity

Answer 4

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?

Answer 5

haven't studied this in years, but still remember parts of it

Answer 6

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?

Answer 7

we need the theorems/definitions

Answer 8

f''(x) < 0 i concave down

Answer 9

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.

Answer 10

is* sorry. My keyboard i being temperamental

Answer 11

for all x in some interval f''(x) <0 is concave down and f''(x) >0 is concave up.

Answer 12

And on a closed interval, you don't necessarily have both a max and a min

Answer 13

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

Answer 14

Hahaha I feel your pain

Answer 15

Can you give me an example where you wouldn't have a maximum and a minimum?

Answer 16

what about a graph that only has the absolute maximum?

Answer 17

Wait, does absolute max and min necessarily mean a real max/min? I'm not sure if I made sense..

Answer 18

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