Bounded Derivative of f(x) = xCos(x) for 0<= x<=5

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    Bounded Derivative
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SUMMARY

The discussion centers on proving that the derivative of the function f(x) = xCos(x) is bounded by 6 for the interval 0 ≤ x ≤ 5. The derivative is calculated as f'(x) = cos(x) + x*sin(x). By evaluating this derivative at the maximum value of x within the specified range, it is established that f'(x) ≤ 1 + 5*1 = 6, confirming the validity of the bound using the intermediate value theorem.

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slippers
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Hi all, my first post so go easy on me! Doing some revision and have been tripped up on a really simple question!

Where f(x) = xCos(x)

Show the bound f '(x)<=6 is valid for 0<= x<=5

I suspect this is an easy solution using the intermediate value theorem!

Thanks in advance,

slippers
 
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f'(x) = cos(x) + x*sin(x) <= 1 + 5*1 = 6
 
Ahhh, something just moved in my brain...

Thanks very much! :D
 

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