Question

if f'(a)=0, then f has a local minimum of a local maximum at a.

Answer 1

That is also false. Just because f'(a) = 0, doesnt guarantee a rel max/min.

Answer 2

Example..take y = x^3

The derivative is 3x^2.

set 3x^2 = 0, you get x = 0.

But x = 0 is not a rel max NOT a rel min.

Answer 3

You can see from the graph of y = x^3, then x = 0 is not a rel max/min, although f ' (0) = 0.

Answer 4

Makes sense?

Answer 5

yes, if it's put in that form it's easier to understand.

Answer 6

True. That's why I broke it down for you, so it is crystal clear.

Answer 7

Thank you very much ^o^!

Answer 8

welcome.