Question

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

Answer 1

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

Answer 2

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

Answer 3

you got the derivative?

Answer 4

no

Answer 5

chain rule

Answer 6

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

Answer 7

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

Answer 8

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