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## Main Question or Discussion Point

I am working my lonely way through Spivack's "Calculus on Manifolds." (not a registered student anywhere, alas).

On p. 23 is a set of problems involving the inner product. I believe I've got it up to d), which asks for a function f:R->R s.t. f is differentiable but |f| is not differentiable.

I believe that |f| is not differentiable for f(x)=x. (if that's wrong I have to start the book all over).

I'm having trouble seeing how to reach this conclusion from consideration of the inner product. |f|**2 = <f,f>, and for g= <f,f>, g' = <x,1> + <1,x>,

F = g**(1/2) = |f|,

and if this is ok so far, I would expect something to be wrong with the next calculation:

F' =(1/2)g**(-1/2)(g') = (1/2)(x**2)**(-1/2) (2x) = 1.

Please help me understand what I've done wrong here. thanks

Ken C

On p. 23 is a set of problems involving the inner product. I believe I've got it up to d), which asks for a function f:R->R s.t. f is differentiable but |f| is not differentiable.

I believe that |f| is not differentiable for f(x)=x. (if that's wrong I have to start the book all over).

I'm having trouble seeing how to reach this conclusion from consideration of the inner product. |f|**2 = <f,f>, and for g= <f,f>, g' = <x,1> + <1,x>,

F = g**(1/2) = |f|,

and if this is ok so far, I would expect something to be wrong with the next calculation:

F' =(1/2)g**(-1/2)(g') = (1/2)(x**2)**(-1/2) (2x) = 1.

Please help me understand what I've done wrong here. thanks

Ken C