If there is still snow/ice on the MR, you will need ice-axe and crampons...and know how to use them, including a lot of practice. Microspikes might be ok for Mt. Baldy, but not the MR on Mt. Whitney.
A climbing helmet is also a good thing to wear, because of loose rock during the time you want to do this.
Check this out:
http://www.summitpost.org/mountaineer-s/155528