\[Find the minimum and maximum values of y=sqrt6theta-sqrt3sec thetaon the interval [0,\frac{\text{pi}}{\text{3}}]\]

djeljenike

djeljenike

Answered question

2021-08-30

Find the minimum and maximum values of y=6θ3secθ
on the interval [0,pi3]

Answer & Explanation

Tuthornt

Tuthornt

Skilled2021-08-31Added 107 answers

y=6θ6secθ on the interval [0,π/3])
f(0)=6
f(π3)=6(π3)3sec(π3)=6(π3)3(2)=0.899
f(x)=63sec(θ)tan(θ)=0
6=3sec(θ)tan(θ)
sec(θ)tan(θ)=63
θ=π4
f(π4)=6(π4)3sec(π4)=0.52566
we have:
f(0)=6=2.4495
f(π3)=0.899
f(π4)=0.52566
minimum =6(ours at x=0)
maximum =0.52566(ours at x=π4)]

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