Find minimum f(x)=\sin(x)+\cos(x)+\sin(2x)+1 for x \in [0,2\pi]

jamessinatraaa

jamessinatraaa

Answered question

2022-01-14

Find minimum f(x)=sin(x)+cos(x)+sin(2x)+1 for x[0,2π]

Answer & Explanation

Anzante2m

Anzante2m

Beginner2022-01-15Added 34 answers

Show that f(t)=t+t2 for t=sin(x)+cos(x). Now recall that t=2sin(x+π4)[2,2] for x[0,2π]. Therefore we reduced the problem to mininization of f(t)=t+t2 on the interval [2,2]. The rest is clear.

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