Question

y= (1/2)x + cosx on the interval -2 pi ≤ x ≤ 2 pi. use the second derivative test ti find the local extrema of f

Answer 1

Answer:

Step-by-step explanation:

y=(1/2)x+cos x

dy/dx=1/2-sin x

dy/dx=0,gives

1/2 -sin x=0

sin x=1/2=sin (π/6),sin (π-π/6)=sinπ/6,sin 5π/6=sin (2nπ+π/6),sin(2nπ+5π/6),n∈ I

d^2y/dx^2=-cos x>0 at x=π/6 and -2π+π/6

or at x=π/6,-11 π/6