find the maximum of the following equation f(x)=1- e^cos(x-1) ([1,2])

Question

anonymous · Answer

i am guessing to take the derivative and find the critical points but maybe there is an easier way

anonymous · Answer

pretty sure this function is increasing on the interval $[1,2]$ making the max at the right hand endpoint

anonymous · Answer

you got the derivative?

anonymous · Answer

no

anonymous · Answer

chain rule

anonymous · Answer

$$f'(x)=\sin(x-1)e^{\cos(x-1)}$$

anonymous · Answer

as $x$ goes from $1$ to $2$ you have  $x-1$ goes from $0$ to $1$
on that interval sine is positive
also $e^{\zeta}$ is always positive
therefore the derivative is positive on the entire interval

anonymous · Answer

therefore function is increasing on that interval
max is at the right hand endpoint, min at the left