Question

Which of the following statements is/are true

1. If f'(c)=0 then f has a local maximum of minimum at x=c
2. 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]
3.The Mean Value theorem can be applied to f(x)=1/x^2 on the interval [1,1]

I think 3 is right,but I'm not sure about the others.
The Options are:
1 only
2 only
1 and 3 only
1 and 2 only

Answer 1

1. Think of f(x) = x^3
2. If f'=0, f does not change.
3. think of f(0). It clearly does not satisfy the MVT on [-1,1]

The typos do not help...

Answer 2

Steve chillll with the typos bro shut up for once and just answer the question