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## Main Question or Discussion Point

help me, please

if f(X) = sin(sin(x)), use a graph to find a upper bound for abs(f

Thanks

if f(X) = sin(sin(x)), use a graph to find a upper bound for abs(f

^{(4)}(x))Thanks

- Thread starter ZuzooVn
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- #1

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help me, please

if f(X) = sin(sin(x)), use a graph to find a upper bound for abs(f^{(4)}(x))

Thanks

if f(X) = sin(sin(x)), use a graph to find a upper bound for abs(f

Thanks

- #2

tiny-tim

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Hi ZuzooVn! Welcome to PF!

ok … draw y = sin(x).if f(X) = sin(sin(x)), use a graph to find a upper bound for abs(f^{(4)}(x))

Now turn the paper sideways and draw x = sin(y) …

what do you get?

- #3

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Would u please tell me more detail about your solution????Hi ZuzooVn! Welcome to PF!

ok … draw y = sin(x).

Now turn the paper sideways and draw x = sin(y) …

what do you get?

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tiny-tim

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HallsofIvy

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tiny-tim has suggested a first step. Have you done it yet?

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yes, i have done it .tiny-tim has suggested a first step. Have you done it yet?

But because i'm a Vietnamese, so my English skill isn't good :D

- #8

HallsofIvy

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Now, tiny-tim, what in the world are you talking about? I'm afraid I dont' see your point either.

I would probably use "brute strength"

If y= sin(sin(x)), then y'= -cos(sin(x))(-cos(x))= cos(x)cos(cos(x)). Now, instead of actually doing the other derivatives (because they get really messy!), use the fact that the nth derivative of (f(x)g(x)) will be [itex]\sum _nC_i f^{i}g^{n-i}[/itex] to see that we will, after three more derivatives, have a sum of 4 terms with binomial coeficients times sin and cos- and the largest possible value for sine or cosine is 1.

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You need to define what fhelp me, please

if f(X) = sin(sin(x)), use a graph to find a upper bound for abs(f^{(4)}(x))

Thanks

- #11

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I means the fourth derivative of fYou need to define what f^{(4)}(x) means. Do you mean, the fourth iteration of f on x, i.e. f o f o f o f (x)? Or do you mean (as others have interpreted) the fourth derivative of f?

- #12

HallsofIvy

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Do you mean least upper bound? I get 8 as an upper bound.

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