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

[slippers]

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

 

[Preno]

f'(x) = cos(x) + x*sin(x) <= 1 + 5*1 = 6

 

[slippers]

Ahhh, something just moved in my brain...

Thanks very much! :D