Finding the relative extrema for a speed function using parametric curves

[chwala]

Homework Statement

Kindly see attached...

Relevant Equations

parametric equations

I have no problem in following the literature on this, i find it pretty easy. My concern is on the derived function, i think the textbook is wrong, it ought to be,
$S^{'}(t)$=$\frac {4t} {\sqrt{1+4t^2}}=0$ is this correct? if so then i guess i have to look for a different textbook to use...

 

[FactChecker]

I agree with you. (Of course, it doesn't change the final answer regarding the relative extrema.)

 

[chwala]

I agree with you. (Of course, it doesn't change the final answer regarding the relative extrema.)

...but the steps have to be correct though! This is Mathematics! I guess its time to ditch the textbook, i would'nt want to spend time on always trying to correct the author..i guess maybe he was drunk when solving this kinda problems...

 

[FactChecker]

An occasional error in a textbook is to be expected and tolerated. Proofreading a book is a never-ending, thankless job. No matter how hard the author tries, there are errors remaining.
Think of it as good practice in spotting errors. As long as the fundamental ideas are presented accurately the book can still be used.

 

[chwala]

An occasional error in a textbook is to be expected and tolerated. Proofreading a book is a never-ending, thankless job. No matter how hard the author tries, there are errors remaining.
Think of it as good practice in spotting errors. As long as the fundamental ideas are presented accurately the book can still be used.

ok mate...i hear you...but if the mistakes seem to be consistent then its a problem...1 or 2 mistakes is understandable.

 

[Delta2]

I know that you probably want a book to be like a holy gospel , that is unmistakable however books are written by humans and humans do mistakes all the time. The average book contains 1 error every like 10 pages or something like that.

 

[chwala]

I know that you probably want a book to be like a holy gospel , that is unmistakable however books are written by humans and humans do mistakes all the time. The average book contains 1 error every like 10 pages or something like that.

True delta, I agree...but there was a book that I used some time back which had wrong solutions throughout for all the given exercises...these are the kind of books I won't use...

 

[Delta2]

True delta, I agree...but there was a book that I used some time back which had wrong solutions throughout for all the given exercises...these are the kind of books I won't use...

Yes, well , I guess there can be some really bad books full of mistakes...

 

[FactChecker]

For worked problems and examples, I have always liked the Schaum's Outline series. They seem to put special emphasis on worked problems. I can not testify to their accuracy, but I do not remember seeing any problems.

 

[chwala]

same mistake here...

 

[Delta2]

yes hehe apparently the mathematician behind this keeps forget that $$(\sqrt {f(x)})'=\frac{1}{2}...$$

 

[chwala]

yes hehe apparently the mathematician behind this keeps forget that $$({\sqrt f(x)})'=\frac{1}{2}...$$