Question

True or False:
A. Absolute maximum is always a maximum.
B. Every absolute maximum (and absolute minimum) is necessarily a critical value.
C. A local minimum (or a local maximum) is always a critical value.
D. Absolutely all functions have a local maximum value.
E. Absolutely all functions have a local maximum value.

Answer 1

Let's do these one at a time.
A. Is an absolute maximum always a maximum?

Answer 2

Okay..I think that's false.

Answer 3

Nope, that's actually correct. An absolute maximum is always a maximum. It's a special type of maximum, but it is always a maximum.

Answer 4

Let's go to B. Is every absolute max/min. is always a critical value?

This one's a little trickier. What do you think?

Answer 5

I think that one's false.

Answer 6

Perfect. You can have graphs that have an absolute maximum, but not critical value.

Answer 7

:)

Answer 8

Now, onto C. Is every local min/max a critical value?

Answer 9

Okay, for C, I think the answer is true.

Answer 10

You're ahead of me there, and you're also correct =D

Answer 11

Awesome!

Answer 12

Last two. Does every function have local maximum value?

Also, is E supposed to be: Does every function have local minimum value?

Answer 13

D: False
E: False
I'm not too sure about these two.

Answer 14

You're still correct! As an example, take the graph of y=x to convince yourself.

Answer 15

Oh yeah, that makes sense! Thank you SO much! You're a life saver!

Answer 16

You're welcome :)