Question

Jika f(x) = 10 + 3 cos 2x, nilai minimum f(x) + f'(x) adalah

Answer 1

F(x) 10 + 3 cos 2x
f '(x) = - 6 sin 2x

f(x) + f'(x) = 10 + 3 cos 2x - 6 sin 2x

k = √(3² + (-6)²) = √(9+36) = √45 = 3√5

Jadi
f(x) + f '(x) = 10 + 3√5 cos (2x - β)

nilai minimum cosinus = - 1
Jadi nilai minimum
f(x) + f '(x) = 10 - 3√5