Which of the following statements is/are true?

If f '(c) = 0, then f has a local maximum or minimum at x = c.
If f is continuous on [a, b] and differentiable on (a, b) and f '(x) = 0 on (a, b), then f is constant on [a, b].
The Mean Value Theorem can be applied to f(x) = 1/x2 on the interval [−1, 1].

I only
II only
I and III only
I and II only

Question

Which of the following statements is/are true?

If f '(c) = 0, then f has a local maximum or minimum at x = c.
If f is continuous on [a, b] and differentiable on (a, b) and f '(x) = 0 on (a, b), then f is constant on [a, b].
The Mean Value Theorem can be applied to f(x) = 1/x2 on the interval [−1, 1].

 I only
 II only
 I and III only
 I and II only

jessereyna · Answer

Ah calculus fun!

trisarahtops · Answer

lo not really. you got any idea?

jessereyna · Answer

1 is true, but i'm not sure about 3

anonymous · Answer

1 is true, 2 is true, and 3 is false. For the Mean Value Theorem to apply, the function must be continuous over the closed interval. I am not sure if you meant 1/(x^2) or 1/2x, but either way the interval includes x=0 which is undefined.

trisarahtops · Answer

so the answer is the last one  I and II only  right?

anonymous · Answer

Yeah, I missed the options at the bottom.

trisarahtops · Answer

what?

anonymous · Answer

I didn't see the answer options you put in the original post, it is I and II only.

trisarahtops · Answer

Thank you ;)