1. ## [SOLVED] True/False about Derivative Graphing

1. If $\displaystyle f'(c)=0$ and $\displaystyle f''(c)>0$, then f(x) has a local minimum at c.
2. If $\displaystyle f'(x)<0$ for all x in (0,1), then f(x) is decreasing on (0,1).
3. A continuous function on a closed interval always attains a maximum and a minimum value.
4. $\displaystyle (f(x) + g(x))' = f'(x)+g'(x)$
5. Continuous functions are always differentiable.
6. If a function has a local maximum at c, then f'(c) exists and is equal to 0.
7. If f(x)=$\displaystyle e^2$, then $\displaystyle f'(x)=2e$

1.T
2.T
3.T
4.T
5.F
6.T
7.F

I know i have exactly one problem wrong, but i can't figure out which one it is.

2. Originally Posted by biermann33
1. If $\displaystyle f'(c)=0$ and $\displaystyle f''(c)>0$, then f(x) has a local minimum at c.
2. If $\displaystyle f'(x)<0$ for all x in (0,1), then f(x) is decreasing on (0,1).
3. A continuous function on a closed interval always attains a maximum and a minimum value.
4. $\displaystyle (f(x) + g(x))' = f'(x)+g'(x)$
5. Continuous functions are always differentiable.
6. If a function has a local maximum at c, then f'(c) exists and is equal to 0.
7. If f(x)=$\displaystyle e^2$, then $\displaystyle f'(x)=2e$