Reading: Cheney & Kincaid, (pp. 563-568 ); Mathematica's 10 min. tutorial (on Mathematica's front end)
The multi-variable case. Suggested Reading: Cheney & Kincaid, (pp. 573-579 ); You are not expected to understand details of methods for the multi-variable case. But you need to know that some of them exist. For "steepest descent/gradient method" you need to have a qualitative idea of what that is. You need to know why the problem of finding a global minimum in many dimensions is so difficult, the "Protein Folding" lecture (above) will help.