Spivak, Calculus - Where to find or is it covered?

[rocomath]

I just got Spivak's book a couple days ago, I've flipped through it and was looking through the Index. Does Spivak cover Related Rates or Optimization? I did not find it at all, so I am curious and wondering if it's under some other name. Thanks!

 

[rudinreader]

I have never seen a calculus book that doesn't mention the f'(x) = 0 for local min/max. That's usually the extend 1-var calculus covers "optimization". The same thing is invariably discussed for multivariable real functions. Related rates are just word problems if I recall correctly. I haven't seen Spivak's book but they say it's semi-advanced, so may not cover word problems, the theoretical one's may be hard enough as it is.

 

[Defennder]

I don't think anyone would recommend Spivak for learning about related rates and optimization. That topic is largely applied calculus, whereas Spivak focuses a lot on theoretical concerns. For applied calculus, I think Stewart's Calculus ought to cover it.

 

[colby2152]

Stewart's it is...

 

[mathwonk]

indeed spivak probably does not cover related rates since there is essentially no new math in it. it is just an example of using the chain rule, but he covers the chain rule quite well. he might cover at least the criteria for existence of and recognition of extrema, but he does not again belabor illustrations of principles like that. at the level of that book, if you know the chain rule and the rolle theorem it is expected you can use them to do word problems.