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

Question

Mathematics

Taniya Combs

13 July, 02:34

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

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Yadiel Cisneros · Answer 1

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