Question

Which of the following statements is/are true?

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

Answer 1

@ganeshie8 @mathstudent55 @kropot72 @Kash_TheSmartGuy

Answer 2

Please help

Answer 3

hint:
for last statement, we have that x=0 belongs to interval [-1,1], and at x=0, the functio
f(x)= 1/x^2 is not continuous

Answer 4

Because it wouldnt exist?

Answer 5

since we can not divide by zero

Answer 6

Sorry, I thought of limits when I said it doesn't exist since like you said, you can't divide by 0

Answer 7

I think A i incorrect as well

Answer 8

yes! I think so, since we can have this case:

Answer 9

I did it algebraically, but got the same thing. I figured if you had f(x) = x^3 then you wouldn't get a max or min anyways, just a hip

Answer 10

So, since A and C are incorrect, the only valid answer would be B, yes?

Answer 11

another counterexample is given by this function:
f(x)= x^3
we have:
f '(x) = 3x^2 and f '(0)==, nevertheless x=0 is not a point of local maximum or minimum