Find the curvature of y=x^3+1.

Question

idealist10 · Answer

@satellite73 @thomaster @ganeshie8 @iambatman @mathstudent55 @freckles @perl @e.mccormick

adamaero · Answer

idealist10 · Answer

$$k(x)=\frac{ \left| y'' \right| }{ [1+(y')^2]^{3/2} }$$

idealist10 · Answer

I know that y'=3x^2 and y"=6x. So I got$$k(x)=\frac{ 6x }{ (1+9x^4)^{3/2} }$$

idealist10 · Answer

But the answer in the book is$$\frac{ 6\left| x \right| }{ (1+9x^4)^{3/2} }$$

idealist10 · Answer

I don't know which answer is right. @ganeshie8 @thomaster

e.mccormick · Answer

How did you get your answer to be out of the | |?

idealist10 · Answer

So the book's answer is right?

e.mccormick · Answer

Well, look a the formula you posted.  There are tules for dealing with | |.  They don't change for calculus...

e.mccormick · Answer

rules that is...

idealist10 · Answer

So the book's answer must be right then, is that correct?

e.mccormick · Answer

If that formula is correct, yes.  Because you can't just take a variable outside of absolute value.

idealist10 · Answer

Okay, thank you!