- #1
ZuzooVn
- 7
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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(4)(x))
Thanks
ZuzooVn said:if f(X) = sin(sin(x)), use a graph to find a upper bound for abs(f(4)(x))
tiny-tim said:Hi ZuzooVn! Welcome to PF!
ok … draw y = sin(x).
Now turn the paper sideways and draw x = sin(y) …
what do you get?
ZuzooVn said:Would u please tell me more detail about your solution?
tiny-tim said:Nope!
Just do it!
HallsofIvy said:tiny-tim has suggested a first step. Have you done it yet?
ZuzooVn said:help me, please
if f(X) = sin(sin(x)), use a graph to find a upper bound for abs(f(4)(x))
Thanks
mXSCNT said:You 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?
Do you mean least upper bound? I get 8 as an upper bound.AUMathTutor said:Unless I made a silly mistake typing things in, it appears that Wolfram Alpha thinks it should be around 3.76.
The function f(x)=sin(sin(x)) is a trigonometric function that takes the sine of the sine of x. It is a periodic function with a period of 2π and its range is between -1 and 1.
To find the fourth derivative of f(x)=sin(sin(x)), you will need to use the chain rule multiple times. The fourth derivative will be a combination of sine and cosine functions.
An upper bound is the smallest possible number that is greater than or equal to a given set of numbers. In other words, it is the maximum value that a function or set of numbers can reach.
To find the upper bound for abs(f(4)(x)) of f(x)=sin(sin(x)), you will need to find the maximum value of the fourth derivative of the function. This can be done by taking the derivative and setting it equal to 0 to find the critical points, and then plugging those points into the fourth derivative to find the maximum value.
Finding the upper bound for abs(f(4)(x)) of f(x)=sin(sin(x)) allows us to determine the maximum rate of change of the function. This information can be useful in understanding the behavior of the function and making predictions about its values.