Question

find the local maxima and local minima for function f of x = sin x minus cos x where X lies between 0 and 2pi​

Answer 1

Answer:

Given f(x) = sin x - cos x, 0 < x < 2π

f'(x) = cos x + sin x,

. .. f'(x) = 0

or cos x + sin x = 0 or tan x = -1

Answer 2

Answer:

f(x) =sinx-cosx ;0<x<2pi

f'(x)=cosx+sinx

f''x=cox-sinx

f'x=0

or cosx=-sinx

or tanx=-1

or, x=3pi/4,7pi/4

at, x=3pi/4,f''x=-root2<0,local maxima point

At x=7pi/4,f"x=+root2>0, local minimal point

Local maxima=f(3pi/4)=root2

Local minima=f(7pi/4)=-root2