Question

true or false :If f has a local maximum at a, then f'(a)=0

Answer 1

f could have a rel max at x = a but f ' (a) will not be 0. f ' (a) could be undefined and yet a will be a rel max.

Answer 2

so this is false. f'(a) can't equal 0 because f already has a as a local max?

Answer 3

It is false becuase f ' (a) doesnt have to equal 0, it can be undefined.

Answer 4

because*

Answer 5

It could be f ' (a) = 0, but not a guarantee.

Answer 6

ah ok ,f'(a) is not definitively equal to zero

Answer 7

correct.

An example would be the function y = 3 - /x/

This function has a rel max at x = 0, but f ' (0) is NOT 0. It is undefined at x = 0.

Answer 8

Look at the graph of y = 3 - /x/.

You can clearly see that the function has a rel max at x = 0. But f ' (o) is NOT 0. It is undefined at x = 0 becuase it has a "sharp corner".

Answer 9

oh ok I get it ^.^!

Answer 10

Thank You!!!!

Answer 11

You're welcome.