I hate true or false i always over think them.

can someone check these and let me know which ones are wrong.

1.. ----F

2.If , then .----F

3.If , then is either a local maximum or a local minimum.----T

4.If for all in , then is decreasing on .----T

5.Differentiable functions are always continuous.----F

6.If and , then has a local minimum at .----F

7.A continuous function on a closed interval always attains a maximum and a minimum value in .----T

Thanks for any help. I really appreciate it.