Question

F(x)=x-2sinx identify the relative extrema

Answer 1

Explanation:

f(x)=x-2 sin x

f'(x)=1-2 cos x

f'(x)=0 gives 1-2 cos x=0

cos x=1/2=cos 60,cos (360-60)

x=60,300

f"(x)=2sin x

at x=60

f"(x)=sin 60=3/2>0

so there is minima.

at x=300

f"(x)=sin 300=sin (360-60)=-sin 60=-3/2<0

so there is maxima .

generalizing

x=300+360n

where n is an integer.

and there is relative minima at x=60+360n where n is an integer.