Question

Nilai maksimum fungsi
y = 1 + sin 2x + cos 2x adalah ....
(A) 2
(B) 1 + √2
(C) 3
(D) 1 + 2√2
(E) 4

Answer 1

Turunan,
Min / Maks, ketika y' = 0
y = 1 + sin 2x + cos 2x
y' = 2cos 2x - 2sin 2x
0 = 2(cos 2x - sin2x)
cos 2x - sin 2x = 0
sin 2x = cos 2x
sin 2x/cos 2x = 1
tan 2x = 1
x = π/8

Substitusikan,
y = 1 + sin 2x + cos 2x
y = 1 + sin(2 π/8) + cos(2 π/8)
y = 1 + sin(π/4) + cos(π/4)
y = 1 + 1/2 √2 + 1/2 √2
y = 1 + √2